Solutions of implicit evolution inclusions with pseudo-monotone mappings

Abstract

Existence results are given for the implicit evolution inclusions $(Bx(t))'+A(t,x(t))\ni f(t)$ and $(Bx(t))'+A(t,x(t))-G(t,x(t))\ni f(t)$ with $B$ a bounded linear operator, $A(t,\cdot)$ a bounded, coercive and pseudo-monotone set-valued mapping and $G$ a set-valued mapping of non-monotone type. Continuity of the solution set of first inclusion with respect to $f$ is also obtained which is used to solve the second inclusion.