Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

Abstract

This paper is mainly concerned with the existence of pseudo Sasymptotically Bloch type periodic solutions to damped evolution equations in Banach spaces. Some existence results for classical Cauchy conditions and nonlocal Cauchy conditions are established through properties of pseudo Sasymptotically Bloch type periodic functions and regularized families. The obtained results show that for each pseudo S-asymptotically Bloch type periodic input forcing disturbance, the output mild solutions to reference equations remain pseudo S-asymptotically Bloch type periodic.