Pseudo almost automorphic solutions for dissipative differential equations in Banach spaces

Abstract

This work aims to study the existence and uniqueness of pseudo compact almost automorphic solution for some dissipative ordinary and functional differential equations. We prove the existence and uniqueness of pseudo compact almost automorphic solution for dissipative differential equations in Banach spaces and then we apply this result to show the existence of pseudo compact almost automorphic solutions for some functional differential equations.

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

“…Such a concept, since its introduction in the literature, has recently generated several developments; see, for example, [8][9][10][11][12] . The question which consists of the existence of pseudo-almost automorphic solutions to abstract partial evolution equations has been made; see for instance 10,11,13 . However, the use of Krasnoselskii fixed point principle to establish the existence of pseudo-almost automorphic solutions to nonautonomous partial evolution equations in the form 1.2 is an original untreated problem, which is the main motivation of the paper.…”

Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities

“…Recently, in [21], the authors extended the works [27] and [28] to almost automorphic case, in fact they proved the existence and uniqueness of a bounded solution on R which is compact almost automorphic. In [15] and [22], the authors studied the existence and uniqueness, attractiveness for a pseudo almost periodic automorphic solution for some general dissipative systems in Banach spaces. Let us indicate the contribution of Zaidman on almost periodic and automorphic functions (see for instance [46][47][48][49]).…”

Pseudo-Almost Automorphic Solutions to Some Second-Order Differential Equations

“…The concept of pseudo almost automorphy is a powerful generalization of both the notion of almost automorphy due to Bochner (see [46]) and that of pseudo almost periodicity due to Zhang (see [21]), which has recently been introduced in the literature by Liang et al [39,52,53]. Such a concept has recently generated several developments and extensions, see, e.g., [18], [20], [29], [30], and [40].…”