Lower semicontinuous perturbations of maximal monotone differential inclusions

Abstract

We prove existence of solutions to $$\dot x \in - Ax + F\left( {t,x} \right),x\left( a \right) = x^0 ,$$ (1) whereA is a maximal monotone operator inRn andF is a multifunction measurable in (t, x) and l.s.c. inx, satisfying a sublinear growth condition.