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

#### Abstract

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

$$u_{i}^{\prime\prime\prime}+au_{i}^{\prime\prime}+bu_{i}^{\prime}+cu_{i}

=f_{i}(t,u_{1}(t),u_{2}(t),\ldots)$$

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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