μ-Pseudo compact almost automorphic weak solutions for some partial functional differential inclusions

Abstract

The aim of this work is to investigate the existence and uniqueness of μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) weak solutions for the following partial functional differential inclusion: where is a strongly maximal monotone operator on a real Hilbert space , is a Stepanov μ-pseudo almost periodic (resp. μ-pseudo compact almost automorphic) function of class r, is the Banach space of all continuous functions from to and the history function is defined by for . Two examples are given for parabolic and subdifferential systems.