Solvability of infinite systems of third-order differential equations in c0 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 x R, R) is.-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.-periodic solutions in Banach sequence space c0. In addition, some examples are supplied to illustrate the usefulness of the outcome.