Application of measure of noncompactness to $\ell_{1}$-solvability of infinite systems of second order differential equations

Abstract

The purpose of this work is to establish a new generalization of Darbo type fixed point theorem using the concept of the so-called $\alpha$-admissibility and the Schauder fixed point theorem. We also include an example which shows that our results are applicable where the previous ones are not. Moreover, we apply our main result to the problem of existence of solutions for a class of infinite systems of second order differential equations.