EXISTENCE RESULTS FOR SEMILINEAR EVOLUTION EQUATIONS INVOLVING MEASURES

Abstract

The goal of this paper is to prove some su±cient conditions for the existence of L1-solutions to a semilinear evolution equation with distributed measures du = (Au)dt + dgu, u(a) =e, where A generates a C0-semigroup in a Banach space X, e in X and u -> gu is a given mapping from L^infty (a, b, X) to BV ([a, b];X).