MEASURE SOLUTIONS FOR EVOLUTION EQUATIONS WITH DISCONTINUOUS VECTOR FIELDS

Abstract

In this paper we present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with the nonlinear part being merely measurable and bounded on bounded sets. This admits discontinuities and exponential growth of the nonlinear term. This is a far reaching generalization of the previous results of the author and others.