Application measure of noncompactness and operator type contraction for solvability of system of differential equations in $\ell_p$-space

Abstract

The aim of this paper is to obtain existence results for an infinite system of second order differential equations in the sequence space $\ell_{p}$ for $1\leq p<\infty$ with the help of a technique associated with measures of noncompactness and contractive condition of operator type. We also provide some illustrative examples in support of our existence theorems.