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

Volume 5, Issue 6, pp 439--447 http://dx.doi.org/10.22436/jnsa.005.06.04

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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.

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Keywords

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

MSC

•  40C05
•  44A10

References

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