| Title:
|
Existence for nonconvex integral inclusions via fixed points (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
293-298 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a nonconvex integral inclusion and we prove a Filippov type existence theorem by using an appropiate norm on the space of selections of the multifunction and a contraction principle for set-valued maps. (English) |
| Keyword:
|
integral inclusions |
| Keyword:
|
contractive set-valued maps |
| Keyword:
|
fixed point |
| MSC:
|
34A60 |
| MSC:
|
45G10 |
| MSC:
|
45N05 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1113.45014 |
| idMR:
|
MR2032102 |
| . |
| Date available:
|
2008-06-06T22:42:23Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107877 |
| . |
| Reference:
|
[1] Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions.LNM 580, Springer, Berlin, 1977. Zbl 0346.46038, MR 0467310 |
| Reference:
|
[2] Cernea A.: A Filippov type existence theorem for infinite horizon operational differential inclusions.Stud. Cerc. Mat. 50 (1998), 15–22. Zbl 1026.34070, MR 1837385 |
| Reference:
|
[3] Cernea A.: An existence theorem for some nonconvex hyperbolic differential inclusions.Mathematica 45(68) (2003), 101–106. Zbl 1084.34508, MR 2056043 |
| Reference:
|
[4] Kannai Z., Tallos P.: Stability of solution sets of differential inclusions.Acta Sci. Math. (Szeged) 63 (1995), 197–207. Zbl 0851.34015, MR 1377359 |
| Reference:
|
[5] Lim T. C.: On fixed point stability for set valued contractive mappings with applications to generalized differential equations.J. Math. Anal. Appl. 110 (1985), 436–441. Zbl 0593.47056, MR 0805266 |
| Reference:
|
[6] Petruşel A.: Integral inclusions. Fixed point approaches.Comment. Math. Prace Mat., 40 (2000), 147–158. Zbl 0991.47041, MR 1810391 |
| Reference:
|
[7] Tallos P.: A Filippov-Gronwall type inequality in infinite dimensional space.Pure Math. Appl. 5 (1994), 355–362. MR 1343457 |
| Reference:
|
[8] Zhu Q. J.: A relaxation theorem for a Banach space integral-inclusion with delays and shifts.J. Math. Anal. Appl. 188 (1994), 1–24. Zbl 0823.34023, MR 1301713 |
| . |
