Geodesic
Application of the infinite matrix theory to the solvability of a system of differential equations
Fares, Ali1 ; Ayad, Ali1
1 Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 439-447.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.005.06.04
Classification : 40C05, 44A10
Keywords: Infinite linear systems of differential equations, systems of linear equations, Laplace operator.

Fares, Ali 1 ; Ayad, Ali 1

1 Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban 
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Fares, Ali; Ayad, Ali. Application of the infinite matrix theory to the solvability of a system of differential equations. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 6, p. 439-447. doi : 10.22436/jnsa.005.06.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.06.04/

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