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

Volume 5, Issue 6, pp 439--447 Publication Date: December 12, 2012
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### 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.

### Keywords

• Infinite linear systems of differential equations
• systems of linear equations
• Laplace operator.

•  40C05
•  44A10

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