Μ-Pseudo compact almost automorphic weak solutions for some partial functional differential inclusions. Issue 18 (12th December 2022) - Ezzinbi, Khalil; Hilal, Khalid; Ziat, Mohamed
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: 1 x ′ ( t ) + A x ( t ) ∋ f ( t, x t ) f o r t ∈ R, where A : H ⟶ 2 H is a strongly maximal monotone operator on a real Hilbert space H, f : R × C ⟶ H is a Stepanov μ -pseudo almost periodic (resp. μ -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 is defined by x t ( θ ) = x ( t + θ ) for θ ∈ [ − r, 0 ] . Two examples are given for parabolic and subdifferential systems.