Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay

Abstract

This paper is concerned with $S$-asymptotically periodic problem of evolution equation with delay in ordered Banach space. Under some weaker assumptions, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed evolution equation, and obtain the existence of maximal and minimal $S$-asymptotically periodic mild solutions. Finally, we give an example to exhibit the practicability of our abstract results.