Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

Abstract

In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

Keywords

• neutral equation
• semigroup
• mild solution
• measure theory
• ergodicity
• μ-pseudo almost periodic functions
• μ-pseudo almost automorphic functions
• sp − μ-pseudo almost periodic functions
• sp − μ-pseudo almost automorphic functions
• banach fixed point theorem