Electron. J. Diff. Equ., Vol. 2016 (2016), No. 48, pp. 1-9.

Existence of solutions to differential inclusions with primal lower nice functions

Nora Fetouci, Mustapha Fateh Yarou

Abstract:
We prove the existence of absolutely continuous solutions to the differential inclusion
$$
 \dot{x}(t)\in F(x(t))+h(t,x(t)),
 $$
where F is an upper semi-continuous set-valued function with compact values such that $F(x(t))\subset \partial f(x(t))$ on [0,T], where f is a primal lower nice function, and h a single valued Caratheodory perturbation.

Submitted June 15, 2015. Published February 10, 2016.
Math Subject Classifications: 34A60, 49J52.
Key Words: Evolution problem; differential inclusion; primal lower nice functions; Carath\'eodory perturbation.

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Nora Fetouci
LMPA Laboratory, Department of Mathematics
Jijel University, Algeria
email: norafetou2005@yahoo.fr
Mustapha Fateh Yarou
LMPA Laboratory, Department of Mathematics
Jijel University, Algeria
email: mfyarou@yahoo.com

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