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

This paper is mainly concerned with the existence of pseudo S -asymptotically 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 S -asymptotically 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.