On a class of innite system of third-order differential equations in lp via measure of noncompactness

E. Pourhadi, M. Mursaleen, R. Saadati


In this paper, with the help of measure of noncompactness together with Darbo-type fixed point theorem, we focus on the infinite system of third-order differential equations
where $ f_{i}\in C(\mathbb{R}\times \mathbb{R}^{\infty}, \mathbb{R}) $ is
$ \omega $-periodic with respect to the first coordinate and $ a,b,c \in \mathbb{R} $ are constants.
The aim of this paper is to obtain the results with respect to the existence of $ \omega $-periodic solutions of the aforementioned system in the Banach sequence space
$ \ell_{p} $ ($ 1\leq p<\infty $) utilizing the respective Green's function.
Furthermore, some examples are provided to support our main results.


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