The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays

We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of...

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Detalles Bibliográficos
Autores principales: Xu, Han, Jin, Yinlai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032758/
https://www.ncbi.nlm.nih.gov/pubmed/24895683
http://dx.doi.org/10.1155/2014/965376
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author Xu, Han
Jin, Yinlai
author_facet Xu, Han
Jin, Yinlai
author_sort Xu, Han
collection PubMed
description We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.
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spelling pubmed-40327582014-06-03 The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays Xu, Han Jin, Yinlai ScientificWorldJournal Research Article We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Hindawi Publishing Corporation 2014 2014-04-16 /pmc/articles/PMC4032758/ /pubmed/24895683 http://dx.doi.org/10.1155/2014/965376 Text en Copyright © 2014 H. Xu and Y. Jin. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Xu, Han
Jin, Yinlai
The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title_full The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title_fullStr The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title_full_unstemmed The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title_short The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
title_sort asymptotic solutions for a class of nonlinear singular perturbed differential systems with time delays
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032758/
https://www.ncbi.nlm.nih.gov/pubmed/24895683
http://dx.doi.org/10.1155/2014/965376
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