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

The aim of this work is to investigate the existence and uniqueness of mu-pseudo almost periodic (resp. mu-pseudo compact almost automorphic) weak solutions for the following partial functional differential inclusion: x '(t) + Ax(t) is an element of f(t, x(t)) for t is an element of R, where A : H -> 2(H) is a strongly maximal monotone operator on a real Hilbert space H, f : R x C -> H is a Stepanov mu-pseudo almost periodic (resp. mu-pseudo compact almost automorphic) function of class r, C = C([-r,0], H) is the Banach space of all continuous functions from [-r, 0] to H and the history function x(t)(theta) = x(t + theta) for theta is an element of[-r, 0]. Two examples are given for parabolic and subdifferential systems.