Existence of solutions of perturbed O.D.E.'s in Banach spaces
Emmanuele, Giovanni
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 463-470 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We consider a perturbed Cauchy problem like the following $$ {\hbox{\rm (PCP)}} \cases x' = A(t,x) +B(t,x) \ x(0)=x_0 \endcases $$ and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).

Publié le : 1991-01-01
Classification:  34A12,  34G05,  34G20,  47H15,  47N20 
@article{118427,
     author = {Giovanni Emmanuele},
     title = {Existence of solutions of perturbed O.D.E.'s in Banach spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {463-470},
     zbl = {0765.34044},
     mrnumber = {1159794},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118427}
}

Emmanuele, Giovanni. Existence of solutions of perturbed O.D.E.'s in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 463-470. http://gdmltest.u-ga.fr/item/118427/

Ambrosetti Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-360. (1967) | MR 0222426

Crandall M.; Pazy A. Nonlinear equations in Banach spaces, Israel J. Math. 11 (1972), 87-94. (1972) | MR 0300166

Deimling K. Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math. 596, Springer Verlag 1977. | MR 0463601 | Zbl 0418.34060

Deimling K. Open Problems for Ordinary Differential Equations in B-Spaces, Proceeding Equa-Diff. 1978, 127-137. | MR 0690603

Diestel J.; Uhl J.J., Jr. Vector Measures, Amer. Math. Soc. 1977. | MR 0453964 | Zbl 0521.46035

Dinculeanu N. Vector Measures, Pergamon Press 1967. | MR 0206190 | Zbl 0647.60062

Dunford N.; Schwartz J.T. Linear Operators, part I, Interscience 1957. | Zbl 0635.47003

Emmanuele G. On a theorem of R.H. Martin on certain Cauchy problems for ordinary differential equations, Proc. Japan Acad. 61 (1985), 207-210. (1985) | MR 0816713 | Zbl 0578.34003

Emmanuele G. Existence of approximate solutions for O.D.E.'s under Carathéodory assumptions in closed, convex sets of Banach spaces, Funkcialaj Ekvacioj, to appear.

Evans L.C. Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math. 26 (1977), 1-42. (1977) | MR 0440431 | Zbl 0349.34043

Hu Shou Chuan Ordinary differential equations involving perturbations in Banach spaces, J. Nonlinear Analysis, TMA 7 (1983), 933-940. (1983) | MR 0713206

Kato T. Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520. (1967) | MR 0226230 | Zbl 0163.38303

Martin R.H. Remarks on ordinary differential equations involving dissipative and compact operators, J. London Math. Soc. 10 (1975), 61-65. (1975) | MR 0369849 | Zbl 0305.34092

Martin R.H. Nonlinear operators and differential equations in Banach spaces, Wiley and Sons 1976. | MR 0492671 | Zbl 0333.47023

Pierre M. Enveloppe d'une famille de semi-groups dans un espace de Banach, C.R. Acad. Sci. Paris 284 (1977), 401-404. (1977) | MR 0440432

Ricceri B.; Villani A. Separability and Scorza-Dragoni's property, Le Matematiche 37 (1982), 156-161. (1982) | MR 0791334

Schechter E. Evolution generated by continuous dissipative plus compact operators, Bull. London Math. Soc. 13 (1981), 303-308. (1981) | MR 0620042 | Zbl 0443.34061

Volkmann P. Ein Existenzsatz für gewöhnliche differentialgleichungen in Banachräumen, Proc. Amer. Math. Soc. 80 (1980), 297-300. (1980) | MR 0577763 | Zbl 0506.34051