Existence of solutions for operator inclusions : a unified approach
Averna, Diego ; Marano, Salvatore A.
Rendiconti del Seminario Matematico della Università di Padova, Tome 102 (1999), p. 285-303 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1999-01-01
@article{RSMUP_1999__102__285_0,
     author = {Averna, Diego and Marano, Salvatore A.},
     title = {Existence of solutions for operator inclusions : a unified approach},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {102},
     year = {1999},
     pages = {285-303},
     mrnumber = {1739543},
     zbl = {0936.47037},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1999__102__285_0}
}

Averna, Diego; Marano, Salvatore A. Existence of solutions for operator inclusions : a unified approach. Rendiconti del Seminario Matematico della Università di Padova, Tome 102 (1999) pp. 285-303. http://gdmltest.u-ga.fr/item/RSMUP_1999__102__285_0/

[1] J.-P. Aubin - A. CELLINA, Differential Inclusions, Springer-Verlag, Berlin (1984). | MR 755330 | Zbl 0538.34007

[2] D. Averna, Lusin type theorems for multifunctions, Scorza Dragoni's property and Carathéodory selections, Boll. Un. Mat. Ital. A (7), 8 (1994), pp. 193-202. | MR 1288374 | Zbl 0817.28007

[3] D. Averna - G. Bonanno, Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side, Ann. Polon. Mat., 71 (1999), pp. 253-271. | MR 1704302 | Zbl 0935.34009

[4] D. Averna - S.A. Marano, Existence theorems for inclusions of the type Ψ(u)(t)∈F(t, Φ(u)(t)), Appl. Anal., to appear. | Zbl 1027.47063

[5] G. Bonanno - S.A. Marano, Higher order ordinary differential equations, Differential Integral Equations, 6 (1993), pp. 1119-1123. | MR 1230485 | Zbl 0785.34021

[6] G. Bonanno - S.A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Nonlinear Anal., 8 (1996), pp. 263-273. | MR 1483627 | Zbl 0891.35038

[7] A. Bressan, Upper and lower semicontinuous differential inclusions: A unified approach, in: H. J. Sussman (ed.), Nonlinear Controllability and Optimal Control, Pure Appl. Math., 133, Dekker, New York (1990), pp. 21-31. | MR 1061382 | Zbl 0704.49011

[8] A. Bressan - G. Colombo, Selections and representations of multifunctions in paracompact spaces, Studia Math., 102 (1992), pp. 209-216. | MR 1170551 | Zbl 0807.54020

[9] M. Day, Normed Linear Spaces, Springer-Verlag, Berlin (1962). | Zbl 0082.10603

[10] K. Deimling, Multivalued Differential Equations, de Gruyter Ser. Nonlinear Anal. Appl. 1, de Gruyter, Berlin (1992). | MR 1189795 | Zbl 0760.34002

[11] C.J. Himmelberg, Measurable relations, Fund. Math., 87 (1975), pp. 53-72. | MR 367142 | Zbl 0296.28003

[12] C.J. Himmelberg - F. S. VAN VLECK, Existence of solutions for generalized differential equations with unbounded right-hand side, J. Differential Equations, 61 (1986), pp. 295-320. | MR 829366 | Zbl 0582.34002

[13] S. Lojasiewicz (jr.), Some theorems of Scorza Dragoni type for multifunctions with application to the problem of existence of solutions for differential multivalued equations, in: C. OLECH - B. JAKUBCZYK - J. ZABCZYK (eds), Mathematical Control Theory, Banach Center Publ., 14, PWN, Warsaw (1985), pp. 625-643. | MR 851255 | Zbl 0576.49024

[14] A. Majorana - S.A. Marano, Boundary value problems for higher order ordinary differential equations, Comment. Math. Univ. Carolin., 35 (1994), pp. 451-466. | MR 1307273 | Zbl 0809.34034

[15] S.A. Marano, Existence theorems for a multivalued boundary value problem, Bull. Austral. Math. Soc., 45 (1992), pp. 249-260. | MR 1155483 | Zbl 0741.34008

[16] O. Naselli RICCERI - B. RICCERI, An existence theorem for inclusions of the type W(u)(t) ∈ F(t, Φ(u)(t)) and application to a multivalued boundary value problem, Appl. Anal., 38 (1990), pp. 259-270. | Zbl 0687.47044

[17] C. Olech, Existence of solutions of non-convex orientor fields, Boll. Un. Mat. Ital. (4), 11 (1975), pp. 189-197. | MR 394372 | Zbl 0322.34002

[18] E. Schechter, A survey of local existence theories for abstract nonlinear initial value problems, in: T. L. GILL - W. W. ZACHARY (eds), Nonlinear Semigroups, Partial Differential Equations and Attractors, Lecture Notes in Math. 1394, Springer-Verlag, Berlin (1987), pp. 136-184. | MR 1021021 | Zbl 0678.34005

[19] A.A. Tolstonogov, Solutions of a differential inclusion with unbounded right-hand side, Siberian Math. J., 29 (1988), pp. 857-868. | MR 971244 | Zbl 0702.34019

[20] R.L. Wheeden - A. Zygmund, Measure and Integral, Monographs Textbooks Pure Appl. Math., 43, Dekker, New York (1977). | MR 492146 | Zbl 0362.26004