Existence and Representation Theorems for a Semilinear Sobolev Equation in Banach Space

Abstract

This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.An existence theory is developed for a semilinear evolution equation in Banach spaceud which is modeled on boundary value problems for partial differential equations of Sobolev type. Theud operators are assumed to be measurable and to satisfy coercive estimates which are not necessarilyud uniform in their time dependence, and to satisfy Lipschitz conditions on the nonlinear term. Applicationsud are briefly indicated