| Title:
|
On a nonconvex boundary value problem for a first order multivalued differential system (English) |
| Author:
|
Cernea, Aurelian |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
237-244 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a boundary value problem for first order nonconvex differential inclusion and we obtain some existence results by using the set-valued contraction principle. (English) |
| Keyword:
|
boundary value problem |
| Keyword:
|
differential inclusion |
| Keyword:
|
contractive set-valued map |
| Keyword:
|
fixed point |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1212.34021 |
| idMR:
|
MR2462979 |
| . |
| Date available:
|
2009-01-29T09:15:08Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119763 |
| . |
| Reference:
|
[1] Boucherif, A., Merabet, N. Chiboub-Fellah: Boundary value problems for first order multivalued differential systems.Arch. Math. (Brno) 41 (2005), 187–195. MR 2164669 |
| Reference:
|
[2] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions.Springer-Verlag, Berlin, 1977. Zbl 0346.46038, MR 0467310 |
| Reference:
|
[3] Cernea, A.: Existence for nonconvex integral inclusions via fixed points.Arch. Math. (Brno) 39 (2003), 293–298. Zbl 1113.45014, MR 2032102 |
| Reference:
|
[4] Cernea, A.: An existence result for nonlinear integrodifferential inclusions.Comm. Appl. Nonlinear Anal. 14 (2007), 17–24. MR 2364691 |
| Reference:
|
[5] Cernea, A.: On the existence of solutions for a higher order differential inclusion without convexity.Electron. J. Qual. Theory Differ. Equ. 8 (2007), 1–8. Zbl 1123.34046, MR 2295686 |
| Reference:
|
[6] Covitz, H., Nadler jr., S. B.: Multivalued contraction mapping in generalized metric spaces.Israel J. Math. 8 (1970), 5–11. MR 0263062, 10.1007/BF02771543 |
| Reference:
|
[7] Kannai, Z., Tallos, P.: Stability of solution sets of differential inclusions.Acta Sci. Math. (Szeged) 61 (1995), 197–207. Zbl 0851.34015, MR 1377359 |
| Reference:
|
[8] 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, 10.1016/0022-247X(85)90306-3 |
| Reference:
|
[9] Tallos, P.: A Filippov-Gronwall type inequality in infinite dimensional space.Pure Math. Appl. 5 (1994), 355–362. MR 1343457 |
| . |
