Pseudo almost periodic solutions in the alpha-norm and Stepanov's sense for some evolution equations

Abstract

UDC 517.9 Our aim is to present the concept of double-measure ergodic and double-measure pseudo almost periodic functions in Stepanov's sense. In addition, we present numerous interesting results, such as the composition theorems and completeness properties for these two spaces of the considered functions. We also establish the existence and uniqueness for the double-measure pseudo almost periodic mild solutions in Stepanov's sense for some evolution equations.