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

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 ΓyΓy on [0,+∞)×X[0,+∞)×X and the semiflow WW generated by the semilinear evolution system on [0,+∞)×X[0,+∞)×X and analysis about all case of impulses, we introduce a reasonable PCPC-mild solution of semilinear evolution equations with impulses at variable times and prove the local and global existence of the PCPC-mild solution and study the maximal existence interval of the solution.