@article{107750,
author = {Lech G\'orniewicz},
title = {Topological structure of solution sets: current results},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {343-382},
zbl = {1090.54014},
mrnumber = {1822805},
language = {en},
url = {http://dml.mathdoc.fr/item/107750}
}
Górniewicz, Lech. Topological structure of solution sets: current results. Archivum Mathematicum, Tome 036 (2000) pp. 343-382. http://gdmltest.u-ga.fr/item/107750/
The solutions set of integral inclusions on the half line, Analysis (2000), 1–7. | MR 1759068
Measures of Noncompactness and Condensing Operators,, (translated from Russian), Birkhauser, Berlin, 1992. (1992) | MR 1153247
On the multivalued Poincaré operators, TMNA 10 (1997), 171–182. (1997) | MR 1646627 | Zbl 0909.47038
Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861–4903. (1999) | MR 1603870
Topological structure of solution sets to multivalued asymptotic problems, Z. Anal. Anwendungen 18, 4 (1999), 1–20. (1999)
Acyclicity of solutions sets to functional inclusions, Nonlinear Analysis TMA (to appear). | MR 1894303
On the Banach contraction principle for multivalued mappings, Lecture Notes in Mathematics (to appear). | MR 1842872
Partially dissipative periodic processes, Banach Center Publ. 35 (1996), 109–118. (1996) | MR 1448430
Multivalued differential equations in a Banach space: an application to control theory, J. Optim. Th. Appl. 21 (1977), 477–486. (1977) | MR 0440144
Le correspondant topologique de l’unicité dans la théorie des équations différentielles, Ann. Math. 43 (1942), 730–738. (1942) | MR 0007195 | Zbl 0061.17106
Continuous dependence on parameters of solutions of operator equations, Trans. Amer. Math. Soc. 231 (1977), 143–166. (1977) | MR 0445351
The solution set to BVP for some functional differential inclusions, Set-Valued Analysis 6 (1998), 257–263. (1998) | MR 1669783
On the solution sets of constrained differential inclusions with applications, Set Valued Anal. (to appear). | MR 1863363 | Zbl 0991.34011
Aronszajn’s theorem for a parabolic partial differential equation, Non-linear Anal. TMA 9, No. 11 (1985), 1183–1187. (1985) | MR 0813652 | Zbl 0583.35053
On the structure of the solution set for periodic boundary value problems, Nonlinear Anal. TMA 4, No. 4 (1980), 821–830. (1980) | MR 0582550 | Zbl 0453.34019
Invariant sets and the Hukuhara–Kneser property for systems of parabolic partial differential equations, Rocky Mount. J. Math. 7, No. 3 (1967), 557–567. (1967) | MR 0600519
Topological approach to differential inclusions on closed sets of $R^n$, , Dynamics Reported 1 (1992), 225–250. (1992)
On the structure of the set of solutions of a functional equation with application to boundary value problems, Ann. Polon. Math. 53, No. 3 (1991), 201–209. (1991) | MR 1109588
Fixed points and properties of solutions of differential inclusions, Math. Sbornik 47 (1983), 895–909 (in Russian). (1983) | MR 0712098
A class of absolute retracts in spaces of integrable functions, Proc. Amer. Math. Soc. 112 (1991), 413–418. (1991) | MR 1045587
Topological degree and nonlinear mappings of analytic type in Banach spaces, J. Math. Anal. Appl. 26 (1969), 730–738. (1969) | MR 0257826 | Zbl 0176.45401
An application of the topological degree theory to the study of the Darboux problem for hyperbolic equations, J. Math. Anal. Appl. 76 (1980), 107–115. (1980) | MR 0586649
Some properties of the set of solutions of a Volterra–Hammerstein integral inclusion, Diff. Uravni. 14, No. 8 (1978), 1043–1048. (1978) | MR 0507406 | Zbl 0433.45018
Certain properties of the set of solutions of the Volterra–Hammerstein integral inclusion, Differents. Uravn. 14, No. 8 (1978), 1465–1472. (1978) | MR 0507406
On the connectedness of sets of solutions of functional inclusions, Mat. Sbornik 119, No. 2 (1982), 295–300. (1982) | MR 0675198
On the existence of solutions of ordinary differential equations in a Banach space, Funkc. Ekvac. 14 (1971), 129–136. (1971) | MR 0304805
On the local existence of solutions of ordinary differential equations, Bull. Acad. Polon. Sci. 20 (1972), 293–296. (1972) | MR 0315237 | Zbl 0255.34053
On the nonexistence of solutions of differential equations in nonreflexive spaces, Bull. Amer. Math. Soc. 78 (1972), 1069–1072. (1972) | MR 0312017
Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space, Nonlinear Anal. TMA 2 (1978), 157–168. (1978) | MR 0512279
An existence theorem for ordinary differential equations in Banach spaces, Bull. Amer. Math. Soc. 77 (1971), 1018–1020. (1971) | MR 0287127
Fundamental theory of contingent differential equations in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 133–144. (1973) | MR 0324162
Some remarks on the structure of the solutions set for differential inclusions in Banach spaces, J. Math. Anal. Appl. 233 (1999), 597–606. (1999) | MR 1689606
Stability of solution sets of differential equations with multivalued right hand side, J. Diff. Equs. 114 (1994), 243–252. (1994) | MR 1302143 | Zbl 0808.34013
On the solvability of systems of noncompact inclusions, Ann. Mat. Pura Appl. (4), 160 (1991), 371–408. (1991) | MR 1163216
On the topological structure of the solution set for a semilinear functional-differential inclusion in a Banach space, (Preprint). | MR 1448435
Perturbations d’inclusions paraboliques par des opérateurs condensants, C. R. Acad. Sci. Paris 320 (1995), Serie I. 1–6. (1995) | MR 1340059
Multi-valued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11. (1970) | MR 0263062
Structure of the set of solutions of an initial-boundary value problem for a parabolic partial differential equations in an unbounded domain, Nonlinear Anal. TMA 27, no. 6 (1996), 723–729. (1996) | MR 1399071
On the structure of fixed point sets of ’k-set contractions’ in $B_0$ spaces, Demonstratio Math. 30 (1997), 233–244. (1997) | MR 1469589
On the structure of fixed point sets of compact maps in $B_0$ spaces with applications to integral and differential equations in unbounded domain, J. Math. Anal. Appl. 154 (1991), 151–163. (1991) | MR 1087965
Properties of the solution set of a generalized differential equations, Bull. Austr. Math. Soc. 6 (1972), 379–389. (1972) | MR 0303023
Existence and stability of solutions for autonomous multivalued differential equations in a Banach space, Rend. Accad. Naz. Lincei, Serie VII, 60 (1976), 767–774. (1976) | MR 0481328
On a property of the unit sphere in a Banach space, Bull. Soc. Math. R. S. Roumaine 21 (1977), 259–262. (1977) | MR 0482402 | Zbl 0365.46015
Characterizations of certain classes of semicontinuous multifunctions by continuous approximations, J. Math. Anal. Appl. 106, No. 1 (1985), 1–8. (1985) | MR 0780314 | Zbl 0574.54012
Topological degree and periodic solutions of differential inclusions, Nonlinear Anal. TMA 37 (1999), 217–245. (1999) | MR 1689752
On the solutions sets for differential inclusions, Bull. Polon. Acad. Sci. 33 (1985), 17–23. (1985) | MR 0798723 | Zbl 0571.34008
n the structure of the set of solutions of the Darboux problem for hyperbolic equations, Proc. Edinburgh Math. Soc., Ser. 2 29, No. 1 (1986), 7–14. (1986) | MR 0829175
On the solution sets of nonconvex differential inclusions, J. Diff. Equs. 128 (1996), 541–555. (1996) | MR 1398331 | Zbl 0853.34013
Solution sets of boundary value problems for nonconvex differential inclusions, Nonlinear Anal. TMA 1 (1993), 303–313. (1993) | MR 1233098 | Zbl 0785.34018
Topological properties of nonconvex differential inclusions of evolution type, Nonlinear Anal. TMA 24 (1995), 711–720. (1995) | MR 1319080
Periodic solutions of differential equations in Banach spaces, Man. Math. 24 (1978), 31–44. (1978) | MR 0499551 | Zbl 0373.34032
Open problems for ordinary differential equations in a Banach space, (in the book: Equationi Differenziali), Florence, 1978. (1978)
On solutions sets of multivalued differential equations, Applicable Analysis 30 (1988), 129–135. (1988)
Solution Sets of Differential Equations in Abstract Spaces, Pitman Research Notes in Mathematics Series, 342, Longman, Harlow, 1996. (1996) | MR 1427944
On the Hukuhara–Kneser property for some Cauchy problems in locally convex topological vector spaces, Lecture Notes in Math. vol. 964, pp. 162–170, Springer, Berlin, 1982. (1982) | MR 0693110 | Zbl 0509.34062
Structure de l’ensemble des solutions du probléme dee Cauchy sous le conditions de Carathéodory, Ann. Sci. Math. Quebec 7 (1983), 5–27. (1983) | MR 0699983
A remark on the Krasnosielskii translation operator, Serdica Math. J. 9 (1983), 102–107. (1983) | MR 0725816
Dimension of the solution set for differential inclusions, Demonstration Math. 26 (1993), 149–158. (1993) | MR 1226553 | Zbl 0783.34008
The topological structure of spaces of solutions of ordinary differential equations, Uspekhi Mat. Nauk 48 (1993), 103–154. (in Russian) (1993) | MR 1227948
On the acyclicity of fixed point sets of multivalued maps, TMNA 14 (1999), 327–343. (1999) | MR 1766183
On the structure of the set of solutions for inclusions with multivalued operators, in Global Analysis - Studies and Applications III, (ed. Yu. G. Borisovich and Yu. E. Glikhlikh), Lecture Notes in Math. vol. 1334, pp. 60–78, Springer, Berlin, 1988. (1988) | MR 0964695
Topological properties of fixed point sets of multivalued maps, Mat. Sb. 188, No. 12 (1997), 33–56. (1997) | MR 1607367
A counter example to Peano’s Theorem in an infinite dimensional Hilbert space, Vestnik Mosk. Gos. Univ., Ser. Mat. Mek. 5 (1972), 31–34. (1972)
Peano’s Theorem in an infinite dimensional Hilbert space is false even in a weakened form, Math. Notes 15 (1974), 273–279. (1974) | MR 0352640
An existence theorem for the equation x = f (t, x) in Banach spaces, Bull. Acad. Polon. Math. 18 (1970), 367–370. (1970) | MR 0269957
Topological approach to differential inclusions, in: A. Granas and H. Frigon eds., NATO ASI Series C 472, Kluwer, 1975. (1975)
Homological methods in fixed point theory of multivalued mappings, Dissertationes Math. 129 (1976), 1–71. (1976)
On the solution sets of differential inclusions, J. Math. Anal. Appl. 113 (1986), 235–244. (1986) | MR 0826673
Topological Fixed Point Theory of Multivalued Mappings, Kluwer, Dordrecht, 1999. (1999) | MR 1748378
On the fixed point set of multivalued contractions, Rend. Circ. Mat. Palermo 40 (1996), 139–145. (1996) | MR 1407087
Fixed points of contractive multivalued maps, Proc. Amer. Math. Soc. 124 (1996), 2675–2683. (1996) | MR 1317038
Differential inclusions on proximate retracts of Hilbert spaces, Int. J. Nonlinear Diff. Equs. TMA 3 (1980), 13–26. (1980)
On the set of solutions of the Darboux problem for some hyperbolic equations, Bull. Acad. Polon. Math. 28, No. 5-6 (1980), 279–286. (1980) | MR 0620202
Topological and differential inclusions, Bull. Austr. Math. Soc. 45 (1992), 177–193. (1992) | MR 1155476
Topological properties of the sets of solutions for functional differential inclusions, Nonlinear Anal. TMA 5, No. 12 (1981), 1349-1366. (1981) | MR 0646220 | Zbl 0496.34041
Continuous dependence of the solutions of an ordinary differential equation, J. Diff. Eqns. 54 (1984), 121–138. (1984) | MR 0757289 | Zbl 0547.34007
On the topological triviality of solution sets, Rocky Mountain J. Math. 10 (1980), 247–252. (1980) | MR 0573874 | Zbl 0456.34004
A note on the solution sets of differential inclusions, Rocky Mountain J. Math. 12 (1982), 621–625. (1982) | MR 0683856 | Zbl 0531.34007
On the topological regularity of the solution set of differential inclusions with constrains, J. Diff. Equat. 107 (1994), 280–289. (1994) | MR 1264523
Sur les systémes des équations differentielles ordinaires, Japan J. Math. 5 (1928), 345–350. (1928)
On decreasing sequence of compact absolute retracts, Fund. Math. 64 (1959), 91–97. (1959) | MR 0253303
On conditions on right hand sides of differential relations, Časopis pro Pěst. Mat. 102 (1977), 334–349. (1977) | MR 0466702
On the Peano Theorem in infinite dimensional spaces, Mat. Zametki 11, No. 5 (1972), 569–576. (1972) | MR 0304808
Condensing multioperators and periodic solutions of parabolic functional - differential inclusions in Banach spaces, Nonlinear Anal. TMA 20 (1991), 781–792. (1991) | MR 1214743
A class of nonlinear boundary value problems without Landesman–Lazer condition, J. Math. Anal. Appl. 105 (1985), 1–11. (1985) | MR 0773569
On Peano’s Theorem in locally convex spaces, Studia Math. 73, No. 3 (1982), 213–223. (1982) | MR 0675425 | Zbl 0507.34047
A Kneser theorem for Volterra integral equations, Proc. Amer. Math. Soc. 40, No. 1 (1973), 183–190. (1973) | MR 0316983 | Zbl 0244.45003
Multivalued differential equations in separable Banach spaces, J. Optim. Th. Appl. 37, No. 2 (1982), 231–249. (1982) | MR 0663523 | Zbl 0458.34008
Über die Lösungen eine system gewöhnlicher differential Gleichungen das der lipschitzchen Bedingung nicht genügt, S. B. Preuss. Akad. Wiss. Phys. Math. Kl. 4 (1923), 171–174. (1923)
Elements of the Theory of Functions and Functional Analysis, Graylock, New York, 1957. (1957) | MR 0085462
Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Heidelberg 1984. (1984) | MR 0736839
Topological and approximation methods in the degree theory of set-valued maps, Dissertationes Math. 336 (1994), 1–102. (1994) | MR 1307460
Kneser’s theorem for multivalued, differential delay equations, Časopis pro Pěst. Mat. 104, No. 1 (1979), 1–8. (1979) | MR 0523570 | Zbl 0405.34059
A generalization of N. Aronszajn’s theorem on connectedness of the fixed point set of a compact mapping, Czech. Math. J. 37, No. 112 (1987), 415–423. (1987) | MR 0904769
On the structure of the fixed point sets of some compact maps in the Fréchet space, Math. Bohemica 118 (1993), 343–358. (1993)
On the structure of the solution set of a functional differential system on an unbounded interval, Arch. Math. (Brno) 35 (1999), 215–228. (1999) | MR 1725839
Structure of the sets of weak solutions of an ordinary differential equation in a Banach space, Ann. Polon. Math. 44, No. 1 (1980), 67–72. (1980) | MR 0764805
Kneser’s Theorem for differential equations in Banach spaces, J. Diff. Equs. 45, No. 2 (1982), 139–147. (1982) | MR 0665991
Kneser’s Theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) (NS) 32, No. 46 (1982), 99–103. (1982) | MR 0710975
The generic property of existence of solutions of differential equations in Banach spaces, J. Diff. Equs. 13 (1973), 1–12. (1973) | MR 0335994
Analyse Non Linéaire Multivoque, Cahiers de Math. de la Decision, Paris, No. 7611, 1977. (1977)
Acyclicité de l’ensemble des solutions de certaines équations fonctionnelles, C. R. Acad. Sci. Paris 282, No. 22A (1976), 1283–1286 | MR 0436195
On fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl. 110 (1985), 436–441. (1985) | MR 0805266
Topological degrees of set-valued compact fields in locally convex spaces, Dissertationes Math. XCII (1972), 1–47. (1972) | MR 0309103
On the set of solutions to a class of nonconvex nonclosed differential inclusions, Acta Math. Hungarica 76 (1997), 287–301. (1997) | MR 1459237 | Zbl 0907.34010
A note on the topological structure of solution sets of Sturm–Liouville problems in Banach spaces, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Math. Nat., (to appear).
Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. TMA 4 (1980), 985–999. (1980) | MR 0586861
On the Cauchy problem for ordinary differential equations in Banach spaces, Arch. Math. 39 (1982), 153–160. (1982) | MR 0675655
On differential inclusions in a Banach space, Soviet Math. Dokl. 15 (1974), 1122–1125. (1974)
Periodic solutions of nonlinear parabolic equations, J. Diff. Equs. 60, No. 1 (1985), 90–102. (1985) | MR 0808259 | Zbl 0537.35049
Nonuniqueness of solutions of semilinear elliptic equations at resonance, Boll. Un. Mat. Ital. 6, 5-A, No. 2, (1986), 205–210. (1986) | MR 0850289
Structure of the solution set for semilinear elliptic equations, Colloq. Math. Soc. Janos Bolyai, 47 (1987), 799–807. (1987) | MR 0890578 | Zbl 0654.35035
Hukuhara–Kneser property for a nonlinear Dirichlet problem, J. Math. Anal. Appl. 128 (1987), 57–63. (1987) | MR 0915966 | Zbl 0648.34019
Decreasing sequences of compact absolute retracts and nonlinear problems, Boll. Un. Mat. Ital. 2-B, No. 7 (1988), 497–507. (1988) | MR 0963315 | Zbl 0667.47035
Aronszajn’s theorem for some nonlinear Dirichlet problem, Proc. Edinburg Math. Soc. 31 (1988), 345–351. (1988) | MR 0969064
Nonlinear second order periodic value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111–128. (1989)
Periodic Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation, Ann. Polon. Math. 54, No. 2 (1991), 111–116. (1991) | MR 1104733 | Zbl 0737.35032
Periodic boundary value problems for some Duffing equations, Diff. and Int. Equs. 1, No. 4 (1988), 399–408. (1988) | MR 0945817
Semilinear functional differential inclusions in a Banach space and controlled parabolic systems, Soviet J. Automat. Inform. Sci. 24, No. 3 (1991), 71–79. (1991) | MR 1173399
On the existence and uniqueness of solutions of an ordinary differential equation in the case of a Banach space, Bull. Acad. Polon. Math. 8 (1969), 667–673. (1969) | MR 0147733
Kneser’s Theorem for differential equations in Banach spaces, Bull. Austral. Math. Soc. 33, No. 3 (1986), 419–434. (1986) | MR 0837488
On the solution set of differential inclusions in a Banach space, Appl. Anal. 25, No. 4 (1987), 319–329. (1987) | MR 0912190
A property of the solution set of differential inclusions in Banach spaces with a Carathéodory orientor field, Appl. Anal. 27, No. 4 (1988), 279–287. (1988) | MR 0936472
On the solution set of differential inclusions with state constraints, Appl. Anal. 31 (1989), 279–289. (1989) | MR 1017517 | Zbl 0698.34015
Convexity of the orientor field and the solution set of a class of evolution inclusions, Math. Slovaca 43 (1993), no. 5, 593–615. (1993) | MR 1273713
On the properties of the solution set of nonconvex evolution inclusions of the subdifferential type, Comment. Math. Univ. Carolin. 34 (1993), no. 4, 673–687. (1993) | MR 1263796 | Zbl 0792.34014
A property of the solution set of nonlinear evolution inclusions with state constraints, Math. Japon. 38 (1993), no. 3, 559–569. (1993) | MR 1221027 | Zbl 0777.34043
On the solution set of nonlinear evolution inclusions depending on a parameter, Publ. Math. Debrecen 44 (1994), no. 1–2, 31–49. (1994) | MR 1269967 | Zbl 0824.34018
On the solution set of nonconvex subdifferential evolution inclusions, Czechoslovak Math. J. 44 (1994), no. 3, 481–500. (1994) | MR 1288166 | Zbl 0868.34010
On the topological regularity of the solution set of differential inclusions with constraints, J. Diff. Equs. 107 (1994), no. 2, 280–289. (1994) | MR 1264523 | Zbl 0796.34017
On the topological properties of the solution set of evolution inclusions involving time-dependent subdifferential operators, Boll. Un. Mat. Ital. 9 (1995), no. 2, 359–374. (1995) | MR 1333967 | Zbl 0845.34066
On the properties of the solution set of semilinear evolution inclusions, Nonlinear Anal. TMA 24 (1995), no. 12, 1683–1712. (1995) | MR 1330643 | Zbl 0831.34014
Topological properties of the solution set of integrodifferential inclusions, Comment. Math. Univ. Carolin. 36 (1995), no. 3, 429–442. (1995) | MR 1364483 | Zbl 0836.34019
On the solution set of nonlinear integrodifferential inclusions in $R^N$, , Math. Japon. 46 (1997), no. 1, 117–127. (1997) | MR 1466124
Topological properties of the solution set of a class of nonlinear evolutions inclusions, Czechoslovak Math. J. 47 (1997), no. 3, 409–424. (1997) | MR 1461421
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Rend. Sem. Mat. Univ. Padova 97 (1997), 163–186. (1997) | MR 1476169 | Zbl 0893.34060
On the structure of the solution set of evolution inclusions with time-dependent subdifferentials, Acta Math. Univ. Comenian. (N.S.) 65 (1996), no. 1, 33–51. (1996) | MR 1422293 | Zbl 0865.34049
Properties of the solution set of nonlinear evolution inclusions, Appl. Math. Optim. 36 (1997), no. 1, 1–20. (1997) | MR 1446789
Sull’integrabilité delle equazioni differenziali del primo ordine, Atti della Reale Accad. dell Scienze di Torino 21 (1886), 677–685.
Démonstration de l’integrabilite des équations differentielles ordinaires, Mat. Annalen 37 (1890), 182–238.
Note on the structure of fixed point sets of 1-set–contractions, Proc. Amer. Math. Soc. 31 (1972), 189–194. (1972) | MR 0285944
Existence of solutions of ordinary differential equations in Banach spaces, Bull. Acad. Polon. Math. 23 (1975), 853–857. (1975) | MR 0393710
On the solution sets for differential inclusions, Boll. Un. Mat. Ital. 7, 6-A (1992), 387–394. (1992) | MR 1196133 | Zbl 0774.34012
Multivalued contractions, Set-Valued Analysis 2, 4 (1994), 559–571. (1994) | MR 1308485 | Zbl 0820.47065
Une propriété topologique de l’ensemble des points fixes d’une contraction multivoque à valeurs convexes, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81 (1987), 283–286. (1987) | MR 0999821
On measures of noncompactness and contracting operators, in Problems in the Mathematical Analysis of Complex Systems, second edition, Voronezh (1968), 89–119. (in Russian) (1968) | MR 0301582
Limit-compact and condensing operators, Uspekh. Mat. Nauk 27 (1972), 1–146. (in Russian) (1972) | MR 0428132
Boundary value problems for second order differential equations in convex subsets in a Banach space, Trans. Amer. Math. Soc. 218 (1976), 397–405. (1976) | MR 0397110
Fredholm mappings and the generalized boundary value problem, Diff. Integral Equs. 8 (1995), 19–40. (1995) | MR 1296108
Generalized boundary value problems and Fredholm mappings, Nonlinear Anal. TMA 30 (1997), 1607-1616. (1997) | MR 1490083
Rδ -set of solutions to a boundary value problem, TMNA, (to appear).
Kneser type theorems for functional differential equations in a Banach space, Funk. Ekvacioj 35 (1992), 451–466. (1992) | MR 1199467 | Zbl 0785.34049
Existence of generalized solutions for ordinary differential equations in Banach spaces, 3. Math. Anal. Appl. 128 (1987), 405–412. (1987) | MR 0917374 | Zbl 0666.34068
Compactness and upper semi continuity of solution set of functional differential equations of hyperbolic type, Comment. Mat. Prace. Mat. 25, No. 2 (1985), 359–362. (1985) | MR 0844652
Qualitative propeties of solutions sets to Lipschitzian differential inclusions, World Sci. Publ. (Singapore 1993), 910–914. (1993) | MR 1242362
Some remarks on ordinary differential equations in Banach spaces, Bull. Acad. Polon. Math. 16 (1968), 795–800. (1968) | MR 0239238
Measure of noncompactness and ordinary differential equations in Banach spaces, Bull Acad. Polon. Sci. 19 (1971), 831–835. (1971) | MR 0303043
Structure of the solutions set of ordinary differential equations in a Banach space, Bull. Acad. Polon. Sci. 21, No. 2 (1973), 141–144. (1973) | MR 0333390
Solutions sets of nonlinear equations, Bull. Acad. Polon. Sci. 21, No. 21 (1973), 971–976. (1973) | MR 0344959
Some properties of the solutions set of ordinary differential equations, Bull. Acad. Polon. Sci. 22, No. 7 (1974), 675–678. (1974) | MR 0355245
On the structure of solutions sets of differential and integral equations in Banach spaces, Ann. Polon. Math. 34 (1977), 165–177. (1977) | MR 0463608
On the equation x = f (t, x) in Banach spaces, Bull. Acad. Polon. Sci. 26, No. 5 (1978), 401–406. (1978) | MR 0499578
Kneser’s theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Bull. Acad. Polon. Sci. 26, No. 5 (1978), 407–413. (1978) | MR 0492684
Sets of fixed points nonlinear mappings in function spaces, Funkcial. Ekvac. 22 (1979), 121–126. (1979) | MR 0551256
On the existence of solutions of differential equations in Banach spaces, Bull. Acad. Polon. Sci. 30, No. 11–12 (1982), 507–515. (1982) | MR 0718727
On the equation x = f (t, x) in locally convex spaces, Math. Nachr. 118 (1984), 179–185. (1984) | MR 0773619
Existence theorems for solutions of integral equations in Banach spaces, Proc. Conf. Diff. Equs. and Optimal Control, Zielona Góra (1985), 101–107. (1985) | MR 0937926
On the application of measure of noncompactness to differential and integral equations in a Banach space, Fasc. Math. 18 (1988), 5–11. (1988) | MR 0988763
The Hukuhara–Kneser property for parabolic systems with nonlinear boundary conditions, J. Math. Anal. 79 (1981), 461–488. (1981) | MR 0606494 | Zbl 0457.35042
The Hukuhara–Kneser property for quasilinear parabolic equations, Non-linear Anal. TMA 12, No. 3 (1988), 231–245. (1988) | MR 0928558 | Zbl 0678.35052
On differential inclusions in a Banach space and continuous selectors, Dokl. Akad. Nauk SSSR 244 (1979), 1088–1092. (1979) | MR 0522051
On properties of solutions of differential inclusions in a Banach space, Dokl. Akad. Nauk SSSR 248 (1979), 42–46. (1979) | MR 0549368 | Zbl 0441.34045
On the structure of the solution set for differential inclusions in a Banach space, Math. Sbornik, 46 (1983), 1–15. (in Russian) (1983) | Zbl 0564.34065
On Peano-phenomenon, Bull. Un. Math. Ital. 3 (1970), 33–42. (1970) | MR 0271793 | Zbl 0179.47101
On the structure of the set of solutions of nonlinear equations, J. Math. Anal. Appl. 34 (1971), 602–617. (1971) | MR 0283645
A fixed point theorem for function spaces, J. Math. Anal. Appl. 36 (1971), 581–587. (1971) | MR 0285945
Existence, uniqueness and approximation of fixed points as a generic property, Bol. Soc. Brasil. Mat. 5 (1974), 17–29. (1974) | MR 0397710
Two remarks on global solutions of ordinary differential equations in the real line, Proc. Amer. Math. Soc. 55 (1976), 111–115. (1976) | MR 0470291 | Zbl 0339.34004
Sur l’existence et l’unicité des integrales des équations différentielles ordinaires au cas de l’espace de Banach, Bull. Acad. Polon. Math. 8 (1960), 301–305. (1960) | MR 0131038 | Zbl 0093.08405
Spaces of solutions, Lect. Notes Op. Res. Math. Econ. vol. 12, Springer-Verlag, (1969), 383–403. (1969) | MR 0361294 | Zbl 0188.15502
A continuous differential equation in a Hilbert space without existence, Funkc. Ekvac. 13 (1970), 19–21. (1970) | MR 0264196
The structure of the solution set of a boundary value problem for a one-dimensional stationary equation of variable type, Chisl. Metody Mekh. Sploshn. Sredy, 15 (1984), 20–30. (1984) | MR 0813536
On the connectivity properties of the solution set of infinitely-parametrized families of vector fields, Boll. Un. Mat. Ital.A (6), 1 (1982), 309–312. (1982) | MR 0663297
On the solution sets of differential inclusion in Banach spaces, Tamkang J. Math., 23 (1992), 59–65. (1992) | MR 1164448 | Zbl 0760.34018
How to make use of the solution set to solve boundary value problems, Recent Trends in Nonlinear Analysis, Birkhäuser, Basel, 2000, 15–25. | MR 1763129 | Zbl 0949.34009
Using solution sets for solving boundary value problems for ordinary differential equations, Nonlinear Anal., 17 (1991), 465–472. (1991) | MR 1124119
The structure of the solution set of the Cauchy problem for a system of generalized ordinary differential equations, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy, 17 (1986), 5–16. (1986) | MR 0853272
On the solution set of maximal monotone differential inclusions in $\mathbb R^m$, Math. Japon., 38 (1993), 91–110. (1993) | MR 1204188
Topological properties of the solution set of integrodifferential inclusions, Comment. Math. Univ. Carolin., 36 (1995), 429–442. (1995) | MR 1364483 | Zbl 0836.34019
A topological property of the solution set to the Sturm–Liouville differential inclusions, Demonstratio Math., 28 (1995), 903–914. (1995) | MR 1392243 | Zbl 0886.47026
Solution set properties for some nonlinear parabolic differential equations, Equadiff IV (Proc. Czechoslovak Conf. Differential Equations and their Applications, Prague, 1977) Springer, Berlin, 1979, 25–30. (1977) | MR 0535319
Convexity of the solution set of a differential inclusion, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., (1998), 21–22. (1998) | MR 1657954
On the solution sets of some nonconvex hyperbolic differential inclusions, Czechoslovak Math. J., 45 (1995), 107–116. (1995) | MR 1314533
On implicit Darboux problem in Banach spaces, Bull. Austral. Math. Soc., 56 (1997), 149–156. (1997) | MR 1464057
On the equation of nth order and the Denjoy integral, Nonlinear Anal., 34 (1998), 1111–1115. (1998) | MR 1637221
A note on the global solutions of the Cauchy problem in Banach spaces, Acta Math. Hung., 88 (2000), 341–346. | MR 1789046
On the structure of solution sets of differential equations in Banach spaces, Math. Slovaca, 50 (2000), 463–471. | MR 1857301
On the equation $x_{ap}^{(n)} = f (t, x)$, Czech. Math. Journal, 46 (1996), 325–330. (1996) | MR 1388620
On nonlinear equations in Banach spaces and axiomatic measures of noncompactness, Funct. Differ. Equ., 5 (1998), 57–68. (1998) | MR 1681184 | Zbl 1049.45013
On the structure of the $L^{p1 ,p2}$ -solution sets of Volterra integral equations in Banach spaces, Comment. Math. Prace Mat., 30 (1991), 253–260. (1991) | MR 1122694 | Zbl 0745.45004
On differential and integral equations in locally convex spaces, Demonstr. Math., 28 (1995), 961–966. (1995) | MR 1392249 | Zbl 0855.34071
On the structure of solution sets of differential and integral equations, and the Perron integral, Proceedings of the Prague Mathematical Conference 1996, Icaris, Prague, 1997, 47–51. (1996) | MR 1703455 | Zbl 0966.34041
Kneser’s theorem for weak solutions of the Darboux problem in Banach spaces, Nonlinear Anal., 20 (1993), 169–173. (1993) | MR 1200387
On the Aronszajn property for differential equations and the Denjoy integral, Comment. Math., 35 (1995), 61–69. (1995) | MR 1384852
On the structure of the solution set of evolution inclusions with Fréchet subdifferentials, J. Appl. Math. Stochastic Anal., 13 (2000), 51–72. | MR 1751029 | Zbl 0966.34052
On the solution set of nonlinear integrodifferential inclusions in $\bold R^N$ , Math. Japon., 46 (1997), 117–127. (1997) | MR 1466124
Topological properties of solution sets for sweeping processes with delay, Portugal. Math., 54 (1997), 485–507. (1997) | MR 1489988 | Zbl 0895.34053
Convexity and the closure of the solution set to differential inclusions, Boll. Un. Mat. Ital. B (7), 4 (1990), 255–263. (1990) | MR 1061215 | Zbl 0719.34031
Continuous selections of solution sets of Lipschitzean differential inclusions, Funkcial. Ekvac., 34 (1991), 321–330. (1991) | MR 1130468
On the stability of solution sets for operational differential inclusions, An. Univ. Timişoara Ser. Ştiinţ. Mat., 29 (1991), 115–124. (1991) | MR 1263091 | Zbl 0799.34016
On the topological structure of the solution set for a semilinear functional-differential inclusion in a Banach space, Topology in Nonlinear Analysis, Polish Acad. Sci., Warsaw, 1996, 159–169. (1996) | MR 1448435
On solution sets of multivalued differential equations, Appl. Anal., 30 (1988), 129–135. (1988) | MR 0967566 | Zbl 0635.34014
Bounds for solution sets of multivalued ODEs, Recent Trends in Differential Equations, World Sci. Publishing, River Edge, NJ, 1992, 127–134. (1992) | MR 1180107 | Zbl 0832.34009
Regularity of solution sets for differential inclusions quasi-concave in a parameter, Appl. Math. Lett., 13 (2000), 31–35. | MR 1750963 | Zbl 0944.34008
The structure of the solution set of a class of nonlinear eigenvalue problems, J. Math. Anal. Appl., 170 (1992), 567–580. (1992) | MR 1188572 | Zbl 0784.35080
On the acyclicity of solution sets of ordinary differential equations, Dokl. Akad. Nauk, 352 (1997), 28–31. (1997) | MR 1445851
On the solution set of the nonconvex sweeping process, Discuss. Math. Differential Incl., 19 (1999), 45–65. (1999) | MR 1758498 | Zbl 0954.34036
Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side, Discuss. Math. Differential Incl., 16 (1996), 103–120. (1996) | MR 1646626 | Zbl 0906.34012
Structure of the solution set of some first order differential equations of comparison type, Trans. Amer. Math. Soc., 160 (1971), 501–512. (1971) | MR 0281995
On the structure of the solution set of $u′′ = f (t, u)$, $u(0) = u(1) = 0$, Math. Nachr., 215 (2000), 103–105. | MR 1768196 | Zbl 0953.34054
On the solution set of nonlinear evolution inclusions, Dynamic Systems Appl., 1 (1992), 71–82. (1992) | MR 1154650 | Zbl 0755.34057
On the properties of the solution set of semilinear evolution inclusions, Nonlinear Anal., 24 (1995), 1683–1712. (1995) | MR 1330643 | Zbl 0831.34014
Topological properties of the solution sets of some differential inclusions, Pure Math. Appl., 10 (1999), 197–223. (1999) | MR 1742594 | Zbl 0977.34008
Essential components and connectedness of solution set for complementarity problems, Fixed Point Theory and Applications (Chinju, 1998), Nova Sci. Publ., Huntington, NY, 2000, 35–46. (1998) | MR 1761212
The measure of the solution set of a linear system with the largest lower exponent, Differentsial’nye Uravneniya, 24 (1988), 2168–2170, 2207. (1988) | MR 0982150
Method of the solution sets for a quasilinear functional-differential inclusion in a Banach space, Differential Equations Dynam. Systems, 4 (1996), 339–350. (1996) | MR 1655630
A note on the solution set of integral inclusions, J. Integral Equations Appl., 12 (2000), 85–94. | MR 1760899
Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged), 61 (1995), 197–207. (1995) | MR 1377359
Continuous dependence of solution sets for generalized differential equations of neutral type, Atti Accad. Sci. Istit. Bologna Cl. Sci. Fis. Rend. (13), 8 (1980/81), 191–195. (1980) | MR 0695193
Compactness and upper semicontinuity of solution set of generalized differential equation in a separable Banach space, Demonstratio Math., 15 (1982), 753–761. (1982) | MR 0693538
Properties of solution set of stochastic inclusions, J. Appl. Math. Stochastic Anal., 6 (1993), 217–235. (1993) | MR 1238600 | Zbl 0796.93106
Quasi-retractive representation of solution sets to stochastic inclusions, J. Appl. Math. Stochastic Anal., 10 (1997), 227–238. (1997) | MR 1468117 | Zbl 1043.34505
On the acyclicity of the solution set of the Cauchy problem for differential equations, Mat. Zametki, 62 (1997). (1997) | MR 1635158
The global solution set for a class of semilinear problems, J. Math. Anal. Appl., 226 (1998), 101–120. (1998) | MR 1646477 | Zbl 0911.34016
Description of the solution set of a linear equation with an interval-defined operator and right-hand side, Dokl. Akad. Nauk, 330 (1993), 430–433. (1993) | MR 1241970
On the parametrization of the solution set of a functional-differential equation, Funct. Differ. Equ., Perm. Politekh. Inst., Perm, (1988), 14–21. (in Russian) (1988) | MR 1066717
On the parametrization of the solution set of a functional-differential equation, Funct. Differ. Equ., 3 (1996), 371–378. (1996) | MR 1459318 | Zbl 0881.34076
Solution sets and boundary value problems in Banach spaces, Topol. Methods Nonlinear Anal., 2 (1993), 179–188. (1993) | MR 1245485 | Zbl 0799.34069
Solution sets of multivalued Sturm–Liouville problems in Banach spaces, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 5 (1994), 161–166. (1994) | MR 1292571 | Zbl 0809.34026
Stability of solution sets for generalized differential equations, J. Math. Anal. Appl., 46 (1974), 289–291. (1974) | MR 0348218 | Zbl 0293.34004
On the structure of the solution set of nonlinear equations, Nonlinear Anal., 7 (1983), 685–693. (1983) | MR 0707077 | Zbl 0519.47037
On the connectivity properties of the solution set of parametrized families of compact vector fields, J. Funct. Anal., 59 (1984), 151–166. (1984) | MR 0766486
On the index and the covering dimension of the solution set of semilinear equations, Nonlinear Functional Analysis and its Applications, Part 2 (Berkeley, Calif., 1983), Amer. Math. Soc., Providence, R.I., 1986, 183–205. (1983) | MR 0843608
On the dimension and the index of the solution set of nonlinear equations, Trans. Amer. Math. Soc., 347 (1995), 835–856. (1995) | MR 1282894
On the solution set of an equation of the type $f (t, \Phi(u)(t)) = 0$, Set-Valued Anal., 4 (1996), 399–405. (1996) | MR 1422403 | Zbl 0873.47041
On the structure of the solution set for first order differential equations, Appl. Math. Comput., 16 (1985), 177–187. (1985) | MR 0780794
Structure of the solution set for semilinear elliptic equations, Differential Equations: Qualitative Theory, Vol. I, II (Szeged, 1984), North-Holland, Amsterdam, 1987, 799–807. (1984) | MR 0890578
On the structure of $L^\varphi $-solution sets of integral equations in Banach spaces, Studia Math., 77 (1984), 465–477. (1984) | MR 0751767
The local structure of the solution set of a first-order nonlinear boundary value problem with constraints at points, Sibirsk. Mat. Zh., 27 (1986), 140–154, 206. (1986) | MR 0873718
On the solution set of evolution inclusions driven by time dependent subdifferentials, Math. Japon., 37 (1992), 1087–1099. (1992) | MR 1196384 | Zbl 0810.34059
Properties of the solution set of evolution inclusions, Nonlinear Anal., 26 (1996), 1279–1292. (1996) | MR 1376103 | Zbl 0849.34017
A topological method for solving nonlinear equations in Banach spaces and some related global results on the structure of the solution sets, Rend. Sem. Mat. Univ. Politec. Torino, 41 (1983), 9–30. (1983) | MR 0778859 | Zbl 0568.47038
The properties of continuity and differentiation of solution sets of Lipschitzean differential inclusions Modeling, Estimation and Control of Systems with Uncertainty (Sopron, 1990), Birkhäuser, Boston, 1991, 349–360. (1990) | MR 1132282
On the topological dimension of the solution set of a class of nonlinear equations, C. R. Acad. Sci. Paris Sér. I Math., 325 (1997), 65–70. (1997) | MR 1461399 | Zbl 0884.47043
A fixed point approach in the study of the solution sets of Lipschitzian functional-differential inclusions, J. Math. Anal. Appl., 160 (1991), 24–46. (1991)
On the structure of the solution set of forced pendulum-type equations, J. Differ. Equ., 131 (1996), 189–208. (1996) | MR 1419011
On the solution set of second-order delay differential inclusions in Banach spaces, Ann. Math. Blaise Pascal, 7 (2000), 65–79. | MR 1769982 | Zbl 0958.34048
The solution set of a differential inclusion on a closed set of a Banach space, Appl. Math., Warsaw, 23 (1995), 13–23. (1995) | MR 1330055 | Zbl 0831.34017
Compactness and upper semicontinuity of solution set of functional-differential equations of hyperbolic type, Comment. Math. Prace Mat., 25 (1985), 359–362. (1985) | MR 0844652 | Zbl 0614.35061
A comparison of the Carathéodory and Filippov solution sets, J. Math. Anal. Appl., 198 (1996), 571–580. (198 ) | MR 1376281
Continuous selections of solution sets to evolution equations, Proc. Amer. Math. Soc., 113 (1991), 403–413. (1991) | MR 1076580 | Zbl 0737.34011
On the solution sets to nonconvex differential inclusions of evolution type, Discrete Contin. Dynam. Systems, 2 (1998), 244–252. (1998) | MR 1722473
Arcwise connectedness of solution sets to Lipschitzean differential inclusions, Boll. Un. Mat. Ital. A (7), 5 (1991), 253–256. (1991) | MR 1120387 | Zbl 0742.34018
Solutions sets of non-linear integral equations, Funkcial. Ekvac., 17 (1974), 67–71. (1974) | MR 0344827
On the structure of solution sets of nonlinear equations, Differential Equations and Optimal Control (Kalsk, 1988), Higher College Engrg., Zielona Góra, 1989, 33–39. (1988) | MR 1067550
On the density and “being boundary” for the solution set of a differential inclusion in a Banach space, Dokl. Akad. Nauk SSSR, 261 (1981), 293–296. (1981) | MR 0638919
The solution set of a differential inclusion in a Banach space. II, Sibirsk. Mat. Zh., 25 (1984), 159–173. (1984) | MR 0732775
The solution set of a differential inclusion in a Banach space. I, Sibirsk. Mat. Zh., 24 (1983), 144–159. (1983) | MR 0731051
Structure of the solution set for a class of nonlinear parabolic problems, Nonlinear Parabolic Equations: Qualitative Properties of Solutions (Rome, 1985), Longman Sci. Tech., Harlow, 1987, 219–225. (1985) | MR 0901112
On the continuous dependence on parameter of the solution set of differential inclusions, Z. Anal. Anwendungen, 11 (1992), 215–220. (1992) | MR 1265929 | Zbl 0783.34010
On a property of the solution set of differential inclusions in a Banach space, Differentsial’nye Uravneniya, 28 (1992), 1346–1351, 1468. (1992) | MR 1203847
Convergence of the solution set of singularly perturbed differential inclusions, Proceedings of the Second World Congress of Nonlinear Analysts, Part 8 (Athens, 1996), Nonlinear Anal., 30 (1997), 5505–5514. (1996) | MR 1726055
Existence of solutions for parabolic type evolution differential inclusions and the property of the solution set, Appl. Math. Mech., 20 (1999), 314–318. (1999) | MR 1704410
On the existence of unbounded connected branches of solution sets of a class of semilinear operator equations, Bull. Soc. Math. Belg. Sér. B, 38 (1986), 14–30. (1986) | MR 0871300
On the solution set of differential inclusions in a Banach space, J. Differ. Equ., 93 (1991), 213–237. (1991) | MR 1125218
The structure of the solution set of a nonlinear elliptic boundary value problem under fixed boundary conditions, Topological and Geometric Methods of Analysis, Voronezh. Gos. Univ., Voronezh, 1989, 152–158, 173. (in Russian) (1989) | MR 1047679