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

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.