A class of semilinear evolution equations with impulses at variable times on Banach spaces

Abstract

In this paper, a general class of semilinear evolution equations with impulses at variable times on infinite-dimensional Banach spaces is considered. Based on a discussion of the relationship between a curve Γ y on [ 0 , + ∞ ) × X and the semiflow W generated by the semilinear evolution system on [ 0 , + ∞ ) × X and analysis about all case of impulses, we introduce a reasonable P C -mild solution of semilinear evolution equations with impulses at variable times and prove the local and global existence of the P C -mild solution and study the maximal existence interval of the solution.