Solvability of infinite systems of third-order differential equations in c 0 by Meir–Keeler condensing operators

Throughout this work, using the technique of measure of noncompactness together with Meir–Keeler condensing operators, we study the solvability of the following infinite system of third-order differential equations in the Banach sequence space c0 as a closed subspace of ℓ∞: ui″′+aui″+bui′+cui=fi(t,u1(t),u2(t),…)where fi∈C(R×R∞,R) is ω-periodic with respect to the first coordinate and a,b,c∈R are constant. Our approach depends on the Green’s function corresponding to the aforesaid system and deduce some conclusions relevant to the existence of ω-periodic solutions in Banach sequence space c0. In addition, some examples are supplied to illustrate the usefulness of the outcome.