A viability result for a first-order differential inclusion

Radouan Morchadi and Saïd Sajid

Abstract: This paper deals with the existence of solutions of a first-order viability problem of the type
$$ \overset{.}{x}\in f(t,x)+F(x), x(t)\in K $$
where $K$ a closed subset of $\R^{n}$, $F$ is upper semicontinuous with compact values contained in the subdifferential $\partial V(x)$ of a convex proper lower semicontinuous function $V$ and $f$ is a Carathéodory single valued map.

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