Application measure of noncompactness and operator type contraction for solvability of an infinite system of differential equations in ℓp-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 ℓp for 1 ≤ p < ∞ 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.