Existence and attractivity of solutions of semilinear Volterra type integro-differential evolution equations

Abstract

In this paper, we prove a result on the existence and local attractivity of solutions of second order semilinear evolution equation. Our investigations will be situated on the Banach space of functions which are defined, continuous and bounded on the nonnegative real axis. The results are obtained by using the Mönch fixed point and the Kuratowski measure of noncompactness. An example is provided to illustrate the main result.

Keywords

• second order semilinear evolution equation
• existence of solutions
• local attractivity of solutions