(1) Department of Mathematics, National Technical University, Zografou Campus, 15773 Athens, Greece;(2) Department of Mathematics, Via Vanvitelli, 1 Perugia, 06123, Italy
Abstract:
In this paper we consider nonlinear-dependent systems with multivalued perturbations in the framework of an evolution triple
of spaces. First we prove a surjectivity result for generalized pseudomonotone operators and then we establish two existence
theorems: the first for a periodic problem and the second for a Cauchy problem. As applications we work out in detail a periodic
nonlinear parabolic partial differential equation and an optimal control problem for a system driven by a nonlinear parabolic
equation.