Abstract

We prove the existence of solutions, 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 the constraint.

Keywords: Multifunction; measurability; selection; functional differential inclusion.

MSC: 34A60, 49J52

Pages:  283$-$291     

Volume  70 ,  Issue  4 ,  2018