Application of measures of noncompactness to the infinite system of second-order differential equations in ℓ p $ell_{p}$ spaces

摘要

In this article, we use the technique based upon measures of noncompactness in conjunction with a Darbo-type fixed point theorem with a view to studying the existence of solutions of infinite systems of second-order differential equations in the Banach sequence space ℓ p $ell_{p}$ . An illustrative example is also given in support of our existence result.