On solutions of a semilinear measure-driven evolution equation with nonlocal conditions on infinite interval

Abstract

This paper studies the existence and asymptotic properties of solutions for a semilinear measure-driven evolution equation with nonlocal conditions on an infinite interval. The existence result of the solutions for the considered equation is established by Schauder's fixed point theorem. Then, the asymptotic stability of solutions is further proved to show that all the solutions may converge to the unique solution of the corresponding Cauchy problem. In addition, under some conditions the existence of global attracting sets and quasi-invariant sets of mild solutions is investigated as well. Finally, an example is provided to illustrate the applications of the obtained results.