Μ-Pseudo compact almost automorphic weak solutions for some partial functional differential inclusions. Issue 18 (12th December 2022)

• Record Type: Journal Article
• Authors: Ezzinbi, Khalil; Hilal, Khalid; Ziat, Mohamed
• Is Part Of: Applicable analysis. Volume 101:Issue 18(2022)
• Page Start: 6388
• Page End: 6410
• Publication Date: 2022-12-12
• Subjects: μ-pseudo almost peridicity -- μ-pseudo compact almost automorphy -- maximal monotone operator -- partial functional differential inclusion -- weak solution; 34C12 -- 34C27 -- 35B15 -- 35B40 -- 35D30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1921747
• Languages: English
• ISSNs: 0003-6811

Abstract

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.