Abstract
In this paper, we study the existence of mild solutions to impulsive integrodifferential evolution equations in Banach spaces. Based on a measure of noncompactness and important properties of semicompact sets, new existence results are obtained. Here the evolution system is only supposed to be strongly continuous, without any compact or equicontinuous assumptions. Some applications are given to illustrate the effectiveness of our results.
Highlights
This paper is concerned with integrodifferential evolution equations with impulsive conditions and nonlocal conditions:
The impulsive differential systems can be used to model processes which are subject to short perturbations whose duration can be negligible in comparison with the duration of the process, such as the dynamics of populations subject to abrupt changes
In [ ], Fan and Li used the techniques of approximate solutions and fixed points to get the mild solutions
Summary
This paper is concerned with integrodifferential evolution equations with impulsive conditions and nonlocal conditions:. Ji et al [ , ] studied the existence and controllability of solutions to impulsive differential system when the semigroup is equicontinuous. Xue [ ] discussed the semilinear nonlocal differential equations when the semigroup T(t) generated by the coefficient operator is compact and the nonlocal function g is not compact. By using a new two-component measure of noncompactness, Benchohra and Ziane [ ] proved the existence of mild solutions for a class of impulsive semilinear evolution differential inclusions with state-dependent delay when A(t) generates a strongly continuous evolution operator.
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