A study on impulsive evolution equation with delay in Banach space

Abstract

This paper is mainly concerned with the existence of the positive mild solutions of impulsive evolution systems with delay in an ordered Banach space. Without assuming the existence of upper and lower solutions, the main results are obtained directly from the characteristics of C0-semigroup T(t)(t ≥ 0) by using monotone
iterative technique and fixed point theorem. At the end, applications to partial differential equations are given.