| Title:
|
On the existence of weak solutions of integral equations in Banach spaces (English) |
| Author:
|
Bugajewski, Dariusz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
35-41 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate weakly continuous solutions of some integral equations in Banach spaces. Moreover, we prove a fixed point theorem which is very useful in our considerations. (English) |
| Keyword:
|
fixed point |
| Keyword:
|
Hammerstein integral equation |
| Keyword:
|
Volterra integral equation |
| Keyword:
|
measure of weak noncompactness |
| Keyword:
|
weak continuity |
| MSC:
|
45G10 |
| MSC:
|
45N05 |
| MSC:
|
47H10 |
| MSC:
|
47H30 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0816.45012 |
| idMR:
|
MR1292580 |
| . |
| Date available:
|
2009-01-08T18:08:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118638 |
| . |
| Reference:
|
[1] Ambrosetti A.: 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] Cramer E., Lakshmikantham V., Mitchell A.R.: On the existence of weak solutions of differential equations in nonreflexive Banach spaces.Nonlinear Analysis 2 (1978), 169-177. Zbl 0379.34041, MR 0512280 |
| Reference:
|
[3] Daneš J.: Some fixed point theorems.Comment. Math. Univ. Carolinae 9 (1968), 223-235. MR 0235435 |
| Reference:
|
[4] De Blasi F.S.: On a property of the unit sphere in a Banach space.Bull. Math. Soc. Sci. Math. R.S. Roumanie 21 (1977), 259-262. Zbl 0365.46015, MR 0482402 |
| Reference:
|
[5] Deimling K.: Ordinary differential equations in Banach spaces.Lecture Notes Math., Berlin-Heidelberg-New York, 1977. Zbl 0418.34060, MR 0463601 |
| Reference:
|
[6] Kuratowski K.: Topology.vol. II, New York-London-Warszawa, 1968. Zbl 0849.01044, MR 0259835 |
| Reference:
|
[7] Szufla S.: On the equation $x'=f(t,x)$ in locally convex spaces.Math. Nachr. 118 (1984), 179-185. Zbl 0569.34052, MR 0773619 |
| Reference:
|
[8] Szufla S.: On the application of measure of noncompactness to existence theorems.Rend. Sem. Mat. Univ. Padova 75 (1986), 1-14. Zbl 0589.45007, MR 0847653 |
| . |
