Lipschitz perturbation to evolution inclusion driven by time-dependent maximal monotone operators

Abstract

An evolution inclusion driven by a time-dependent maximal monotone operator and a Lipschitz closed valued perturbation, in a separable Hilbert space is considered. The inclusion with a convexified perturbation term is also studied. Then, the existence of solutions and the relaxation property between these evolution inclusions are proved. Applications to dynamical systems governed by a couple of a fractional equation and an evolution inclusion involving time-dependent maximal monotone operators with a Lipschitz perturbation are presented.