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 p 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.

Nonlinear Sequential Caputo and Caputo-Hadamard Fractional Differential Equations with Dirichlet Boundary Conditions in Banach Spaces

“…The authors obtained the existence of solutions by using the Hausdorff measure of noncompactness and Darbo type fixed point theorem. Additionally, for more interesting details about infinite systems of differential equations or integral equations in some Banach sequence spaces we suggest some works [5,[32][33][34][35][36][37][38]. Moreover, the reader is advised to see the recent book [12] where several applications of the measure of noncompactness can be found.…”