This paper is concerned with the existence mild solutions of second order semilinear evolution equation in Banach space. The results are obtained by using the fixed point technique and Kuratowski measure of noncompactness. We give an example for illustration.

Abstract:In this paper, we shall establish su cient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdor measure, noncompactness and Tikhono 's xed point theorem. We give an example for illustration.

We consider a non-instantaneous system represented by a second order nonlinear differential equation in a Banach space E. We use the family of linear bounded operators introduced by Kozak, Darbo fixed point method and Kuratowski measure of noncompactness. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.