| Title:
|
On the Volterra integral equation and axiomatic measures of weak noncompactness (English) |
| Author:
|
Bugajewski, Dariusz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
183-190 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a set of weak solutions of the nonlinear Volterra integral equation has the Kneser property. The main condition in our result is formulated in terms of axiomatic measures of weak noncompactness. (English) |
| Keyword:
|
measure of weak noncompactness |
| Keyword:
|
Volterra integral equation |
| Keyword:
|
nonlinear Volterra integral equation |
| Keyword:
|
Kneser property |
| MSC:
|
45D05 |
| MSC:
|
45G10 |
| MSC:
|
47H09 |
| idZBL:
|
Zbl 0982.45002 |
| idMR:
|
MR1826481 |
| DOI:
|
10.21136/MB.2001.133913 |
| . |
| Date available:
|
2009-09-24T21:48:49Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133913 |
| . |
| Reference:
|
[1] A. Ambrosetti: Un teorema di esistenza per le equazioni differenziali negli spazi di Banach.Rend. Sem. Mat. Univ. Padova 39 (1967), 349–360. MR 0222426 |
| Reference:
|
[2] J. Banaś, J. Rivero: On measures of weak noncompactness.Ann. Mat. Pura Appl. 151 (1988), 213–224. MR 0964510, 10.1007/BF01762795 |
| Reference:
|
[3] D. Bugajewski: On the existence of weak solutions of integral equations in Banach spaces.Comment. Math. Univ. Carolin. 35 (1994), 35–41. MR 1292580 |
| Reference:
|
[4] D. Bugajewski, S. Szufla: Kneser’s theorem for weak solutions of the Darboux problem in Banach spaces.Nonlinear Anal. 20 (1993), 169–173. MR 1200387, 10.1016/0362-546X(93)90015-K |
| Reference:
|
[5] E. Cramer, V. Lakshmikantham, A. R. Mitchell: On the existence of weak solutions of differential equations in nonreflexive Banach spaces.Nonlinear Anal. 2 (1978), 169–177. MR 0512280, 10.1016/0362-546X(78)90063-9 |
| Reference:
|
[6] F. S. De Blasi: On a property of the unit sphere in Banach spaces.Bull. Math. Soc. Sci. Math. Roum. 21 (1977), 259–262. MR 0482402 |
| Reference:
|
[7] G. Emanuelle: Measures of weak noncompactness and fixed point theorems.Bull. Math. Soc. Sci. Math. Roum. 25 (1981), 353–358. |
| Reference:
|
[8] J. L. Kelley, I. Namioka: Linear Topological Spaces.Van Nostrand, Princeton, 1963. MR 0166578 |
| Reference:
|
[9] M. A. Krasnosel’skij, S. G. Krein: To the theory of ordinary differential equations in Banach spaces.Trudy Sem. Funk. Anal. Voronezh. Univ. 2 (1956), 3–23. (Russian) MR 0086191 |
| Reference:
|
[10] D. O’Regan: Integral equations in reflexive Banach spaces and weak topologies.Proc. Amer. Math. Soc. 124 (1996), 607–614. MR 1301043, 10.1090/S0002-9939-96-03154-1 |
| Reference:
|
[11] A. Szép: Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces.Studia Sci. Math. Hungarica 6 (1971), 197–203. MR 0330688 |
| . |
