TY - JOUR
T1 - Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space
AU - Sheng , Lixin
AU - Hu , Weimin
AU - Su , You-Hui
AU - Yun , Yongzhen
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 194
EP - 209
PY - 2024
DA - 2024/03
SN - 6
DO - http://doi.org/10.12150/jnma.2024.194
UR - https://global-sci.org/intro/article_detail/jnma/22975.html
KW - Impulsive evolution equation, approximate controllability, nonlocal conditions, resolvent operator, evolution family.
AB - <p style="text-align: justify;">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.</p>