Application of the infinite matrix theory to the solvability of a system of differential equations


Authors

Ali Fares - Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban. Ali Ayad - Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban.


Abstract

In this paper we deal with the solvability of the infinite system of differential equations \(x'(t) = \Delta(\lambda)x(t) + b\) with \(x(0) = a\), where \(\Delta(\lambda)\) is the triangle defined by the infinite matrix whose the nonzero entries are \([\Delta(\lambda)]_{nn} = \lambda_n\) and \([\Delta(\lambda)]_{n,n-1} = \lambda_{n-1}\) for all \(n \in \mathbb{N}\), for a given sequence \(\lambda\) and \(a, b\) are two given infinite column matrices. We use a new method based on Laplace transformations to solve this system.


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