| Title:
|
Existence of solutions of perturbed O.D.E.'s in Banach spaces (English) |
| Author:
|
Emmanuele, Giovanni |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1991 |
| Pages:
|
463-470 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]). (English) |
| Keyword:
|
perturbed Cauchy problem |
| Keyword:
|
semi-inner product |
| Keyword:
|
measure of noncompactness |
| MSC:
|
34A12 |
| MSC:
|
34G05 |
| MSC:
|
34G20 |
| MSC:
|
47H15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0765.34044 |
| idMR:
|
MR1159794 |
| . |
| Date available:
|
2009-01-08T17:46:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118427 |
| . |
| Reference:
|
[1] Ambrosetti: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach.Rend. Sem. Univ. Padova 39 (1967), 349-360. MR 0222426 |
| Reference:
|
[2] Crandall M., Pazy A.: Nonlinear equations in Banach spaces.Israel J. Math. 11 (1972), 87-94. MR 0300166 |
| Reference:
|
[3] Deimling K.: Ordinary Differential Equations in Banach Spaces.Lecture Notes in Math. 596, Springer Verlag 1977. Zbl 0418.34060, MR 0463601 |
| Reference:
|
[4] Deimling K.: Open Problems for Ordinary Differential Equations in B-Spaces.Proceeding Equa-Diff. 1978, 127-137. MR 0690603 |
| Reference:
|
[5] Diestel J., Uhl J.J., jr.: Vector Measures.Amer. Math. Soc. 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
[6] Dinculeanu N.: Vector Measures.Pergamon Press 1967. Zbl 0647.60062, MR 0206190 |
| Reference:
|
[7] Dunford N., Schwartz J.T.: Linear Operators.part I, Interscience 1957. Zbl 0635.47003 |
| Reference:
|
[8] Emmanuele G.: On a theorem of R.H. Martin on certain Cauchy problems for ordinary differential equations.Proc. Japan Acad. 61 (1985), 207-210. Zbl 0578.34003, MR 0816713 |
| Reference:
|
[9] 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. |
| Reference:
|
[10] Evans L.C.: Nonlinear evolution equations in an arbitrary Banach space.Israel J. Math. 26 (1977), 1-42. Zbl 0349.34043, MR 0440431 |
| Reference:
|
[11] Hu Shou Chuan: Ordinary differential equations involving perturbations in Banach spaces.J. Nonlinear Analysis, TMA 7 (1983), 933-940. MR 0713206 |
| Reference:
|
[12] Kato T.: Nonlinear semigroups and evolution equations.J. Math. Soc. Japan 19 (1967), 508-520. Zbl 0163.38303, MR 0226230 |
| Reference:
|
[13] Martin R.H.: Remarks on ordinary differential equations involving dissipative and compact operators.J. London Math. Soc. 10 (1975), 61-65. Zbl 0305.34092, MR 0369849 |
| Reference:
|
[14] Martin R.H.: Nonlinear operators and differential equations in Banach spaces.Wiley and Sons 1976. Zbl 0333.47023, MR 0492671 |
| Reference:
|
[15] Pierre M.: Enveloppe d'une famille de semi-groups dans un espace de Banach.C.R. Acad. Sci. Paris 284 (1977), 401-404. MR 0440432 |
| Reference:
|
[16] Ricceri B., Villani A.: Separability and Scorza-Dragoni's property.Le Matematiche 37 (1982), 156-161. MR 0791334 |
| Reference:
|
[17] Schechter E.: Evolution generated by continuous dissipative plus compact operators.Bull. London Math. Soc. 13 (1981), 303-308. Zbl 0443.34061, MR 0620042 |
| Reference:
|
[18] Volkmann P.: Ein Existenzsatz für gewöhnliche differentialgleichungen in Banachräumen.Proc. Amer. Math. Soc. 80 (1980), 297-300. Zbl 0506.34051, MR 0577763 |
| . |
