On viability result for first-order functional differential inclusions

Abstract

We prove the existence ofsolutions, in separable Banach spaces, for the following differential inclusion:$$\begin{array}{r}\{\begin{array}{llll}\dot{x}(t)\in F(t,T(t)x),& \text{a.e. on }[0,\tau ];x(s)=\phi (s),& \mathrm{\forall }s\in [-a,0];x(t)\in C(t),& \mathrm{\forall }t\in [0,\tau ];\end{array}\end{array}$$We consider weaker hypotheses on theconstraint.