On viability result for first-order functional differential inclusions

Abstract

We prove the existence ofsolutions, in separable Banach spaces, for the following differential inclusion:\begin{align*}\left\{\begin{array}{ll}\dot{x}(t) \in F(t,T(t)x),\quad &\mbox{a.e. on }[0,\tau]; x(s)=\varphi(s),\quad &\forall s\in [-a,0]; x(t) \in C(t),\quad &\forall t\in [0,\tau];\end{array}\right.\end{align*}We consider weaker hypotheses on theconstraint.