Abstract

We prove the existence of a continuous selection of the multivalued map φ→Φ(φ) which is the set of all mild solutions of the evolution inclusion x(t)∈Ax(t)+F(t,x(t))+∫0th(t−s)g(x(s))dsx(0)=φ. Here F is a multivalued map, Lipschitzian with respect to x, and A is the infinitesimal generator of a C0-semigroup.