Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space
Year: 2024
Author: Lixin Sheng, Weimin Hu, You-Hui Su, Yongzhen Yun
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 194–209
Abstract
In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii’s fixed point theorem, the theory of evolution family and the resolvent operator. In particular, the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.194
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 1 : pp. 194–209
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Impulsive evolution equation approximate controllability nonlocal conditions resolvent operator evolution family.