# Nonconvex and nonmonotone perturbations of evolution inclusions of subdifferential type

Research paper by N. S. Papageorgiou

Indexed on: 01 Jun '90Published on: 01 Jun '90Published in: Periodica Mathematica Hungarica

#### Abstract

In this paper we prove the existence of strong solutions for evolution inclusions of the form −$$\dot x$$(t) ∈ ∂ϕ(x(t))+F(t,x)) defined in a separable Hilbert space, where ∂ϕ(·) denotes the subdifferential of a proper, closed, convex function ϕ(·) andF(t,x) is a multivalued nonconvex, nonmonotone perturbation satisfying a general growth condition.