Viability problem with perturbation in Hilbert space

A. Ait, University Hassan II-Mohammedia, Mohammedia, Morocco
S. Sajid, University Hassan II-Mohammedia, Mohammedia, Morocco

E. J. Qualitative Theory of Diff. Equ., No. 7. (2007), pp. 1-14.

Abstract: This paper deals with the existence result of viable solutions of the differential inclusion \begin{center}$\dot{x}(t) \in f(t,x(t)) + F(x(t))$\\$x(t) \in K$ on $[0,T],$ \end{center} where $K$ is a locally compact subset in separable Hilbert space $H,$ $(f(s,\cdot))_s$ is an equicontinuous family of measurable functions with respect to $s$ and $F$ is an upper semi-continuous set-valued mapping with compact values contained in the Clarke subdifferential $\partial_{c} V(x)$ of an uniformly regular function $V.$

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