Resumen de A Study on Asymptotically Periodic Behavior for Evolution Equations with Delay in Banach Spaces

Haide Gou, Yongxiang Li

• The goal of this paper is to consider abstract evolution equation with delay in the framework of ordered Banach spaces. Firstly, we investigate the existence of minimal positive S-asymptotically -periodic mild solution for abstract evolution equation with delay on infinite interval. Secondly, based on monotone iterative technique coupled with fixed point theorem, the existence of minimal positive S-asymptotically -periodic mild solution is discussed without assuming the existence of upper and lower solutions in the sense of compact and noncompact semigroups. At the end, applications to partial differential equations are given.