Weyl double-measure pseudo almost automorphic functions and Weyl double-measure pseudo almost automorphic solutions to a semilinear abstract differential equations

TL;DR

This paper introduces Weyl double-measure pseudo-almost automorphic functions and proves the existence, uniqueness, and stability of their solutions in semilinear abstract differential equations.

Contribution

It develops a new class of functions and applies fixed point theorems to establish solution properties for semilinear differential equations.

Findings

Existence and uniqueness of solutions proven.

Global exponential stability established.

New function class introduced and characterized.

Abstract

This paper first propose a concept of Weyl double-measure pseudo-almost automorphic functions and examines their fundamental characteristics. Subsequently, employing fixed point theorems, we systematically investigate the existence and uniqueness of both Weyl almost automorphic solutions and Weyl double-measure pseudo-almost automorphic solutions for a class of semilinear abstract differential equations. Finally, through the application of inequality-based analytical methods, we establish the global exponential stability of these solutions.