Solvability of Infinite Systems of Third Order Differential Equations in a Sequence Space $n ( \phi)$ via Measures of Non-Compactness

This paper establishes the necessary conditions for the existence of $\omega$-periodic solutions in the sequence space $n(\phi)$ for an infinite system of third-order differential equations. The analysis utilizes the system's Green's function, the Meir-Keeler condensing operator, and measures of non-compactness. To illustrate our results, we provide relevant examples.