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2015 Algebrization of Nonautonomous Differential Equations
María Aracelia Alcorta-García, Martín Eduardo Frías-Armenta, María Esther Grimaldo-Reyna, Elifalet López-González
J. Appl. Math. 2015: 1-10 (2015). DOI: 10.1155/2015/632150

Abstract

Given a planar system of nonautonomous ordinary differential equations, d w / d t = F ( t , w ) , conditions are given for the existence of an associative commutative unital algebra A with unit e and a function H : Ω R 2 × R 2 R 2 on an open set Ω such that F ( t , w ) = H ( t e , w ) and the maps H 1 ( τ ) = H ( τ , ξ ) and H 2 ( ξ ) = H ( τ , ξ ) are Lorch differentiable with respect to A for all ( τ , ξ ) Ω , where τ and ξ represent variables in A . Under these conditions the solutions ξ ( τ ) of the differential equation d ξ / d τ = H ( τ , ξ ) over A define solutions ( x ( t ) , y ( t ) ) = ξ ( t e ) of the planar system.

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María Aracelia Alcorta-García. Martín Eduardo Frías-Armenta. María Esther Grimaldo-Reyna. Elifalet López-González. "Algebrization of Nonautonomous Differential Equations." J. Appl. Math. 2015 1 - 10, 2015. https://doi.org/10.1155/2015/632150

Information

Published: 2015
First available in Project Euclid: 14 December 2015

zbMATH: 1382.12002
MathSciNet: MR3426648
Digital Object Identifier: 10.1155/2015/632150

Rights: Copyright © 2015 Hindawi

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