Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space (Journal of Nonlinear Modeling and Analysis, 2024)
In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations withnonlocal conditions in Banach space. The existence of mild solutions and someconditions for approximate controllability of these non-autonomous impulsiveevolution equations are given by using the Krasnoselskii’s fixed point theorem,the theory of evolution family and the resolvent operator. In particular, theimpulsive functions are supposed to be continuous and the nonlocal item isdivided into Lipschitz continuous and completely bounded. An example isgiven as an application of the results.
Keywords: Impulsive evolution equation; approximate controllability; nonlocal conditions; resolvent operator; evolution family.