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 c 0 as a closed subspace of ℓ ∞ : u i ″ ′ + a u i ″ + b u i ′ + c u i = f i ( t , u 1 ( t ) , u 2 ( t ) , … ) where f i ∈ 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 c 0 . In addition, some examples are supplied to illustrate the usefulness of the outcome.