The solution manifolds of impulsive differential equations

Abstract

In this paper, we investigate a class of impulsive differential equations with state-dependent delay under analytic semigroup in Banach spaces. The existence and uniqueness of classical solution is obtained under the assumptions that nonlinear function and impulsive map are Lipschitz continuous. On these assumptions, we further study the existence and smoothness of solution manifold of impulsive differential equations with state-dependent delay.