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Article

Keywords:
boundary value problem; differential inclusion; contractive set-valued map; fixed point
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.
References:
[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
[2] Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Springer-Verlag, Berlin, 1977. MR 0467310 | Zbl 0346.46038
[3] Cernea, A.: Existence for nonconvex integral inclusions via fixed points. Arch. Math. (Brno) 39 (2003), 293–298. MR 2032102 | Zbl 1113.45014
[4] Cernea, A.: An existence result for nonlinear integrodifferential inclusions. Comm. Appl. Nonlinear Anal. 14 (2007), 17–24. MR 2364691
[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. MR 2295686 | Zbl 1123.34046
[6] Covitz, H., Nadler jr., S. B.: Multivalued contraction mapping in generalized metric spaces. Israel J. Math. 8 (1970), 5–11. DOI 10.1007/BF02771543 | MR 0263062
[7] Kannai, Z., Tallos, P.: Stability of solution sets of differential inclusions. Acta Sci. Math. (Szeged) 61 (1995), 197–207. MR 1377359 | Zbl 0851.34015
[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. DOI 10.1016/0022-247X(85)90306-3 | MR 0805266 | Zbl 0593.47056
[9] Tallos, P.: A Filippov-Gronwall type inequality in infinite dimensional space. Pure Math. Appl. 5 (1994), 355–362. MR 1343457
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