Solutions of Cauchy and periodic problems for evolution inclusions with multi-valued $w_{{\lambda }_0}$-pseudomonotone maps

Abstract

We consider differential-operator inclusions with $w_{{\lambda }_0}$-pseudomonotone multi-valued maps. The problem of investigation of solutions of Cauchy and periodic problems is solved by Faedo–Galerkin (FG) method. Important a priori estimates are obtained. Some topological descriptions of the resolvent operators are made.