Existence and controllability results for non-densely defined impulsive semilinear functional differential equations

Abstract

In this paper, we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some non-densely defined impulsive semilinear functional differential equations in separable Banach spaces. We shall rely on a fixed point theorem for the sum of completely continuous and contraction operators. The question of controllability of these equations are also considered.