Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II

In this paper we study the asymptotic integration problem in the neighborhood of infinity for a certain class of linear functional differential systems. We construct the asymptotics for the solutions of the considered systems in a critical case. In the second part of the work we establish the existe...

Full description

Saved in:
Bibliographic Details
Main Author: P. N. Nesterov
Format: Article
Language:English
Published: Yaroslavl State University 2014-10-01
Series:Моделирование и анализ информационных систем
Subjects:
Online Access:https://www.mais-journal.ru/jour/article/view/82
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849338719400624128
author P. N. Nesterov
author_facet P. N. Nesterov
author_sort P. N. Nesterov
collection DOAJ
description In this paper we study the asymptotic integration problem in the neighborhood of infinity for a certain class of linear functional differential systems. We construct the asymptotics for the solutions of the considered systems in a critical case. In the second part of the work we establish the existence of a critical manifold for the considered class of systems and study its main properties. We also investigate the asymptotic integration problem for a reduced system. We illustrate the proposed method with an example of constructing the asymptotics for the solutions of a certain scalar delay differential equation.
format Article
id doaj-art-dc3c6a5337a74b24b0d3638f611c2e50
institution Kabale University
issn 1818-1015
2313-5417
language English
publishDate 2014-10-01
publisher Yaroslavl State University
record_format Article
series Моделирование и анализ информационных систем
spelling doaj-art-dc3c6a5337a74b24b0d3638f611c2e502025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172014-10-0121553710.18255/1818-1015-2014-5-5-3776Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. IIP. N. Nesterov0P.G. Demidov Yaroslavl State UniversityIn this paper we study the asymptotic integration problem in the neighborhood of infinity for a certain class of linear functional differential systems. We construct the asymptotics for the solutions of the considered systems in a critical case. In the second part of the work we establish the existence of a critical manifold for the considered class of systems and study its main properties. We also investigate the asymptotic integration problem for a reduced system. We illustrate the proposed method with an example of constructing the asymptotics for the solutions of a certain scalar delay differential equation.https://www.mais-journal.ru/jour/article/view/82functional-differential equationscritical manifoldasymptotic integrationaveraging methodlevinson’s theorem
spellingShingle P. N. Nesterov
Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
Моделирование и анализ информационных систем
functional-differential equations
critical manifold
asymptotic integration
averaging method
levinson’s theorem
title Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
title_full Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
title_fullStr Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
title_full_unstemmed Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
title_short Center Manifold Method in the Asymptotic Integration Problem for Functional Differential Equations with Oscillatory Decreasing Coefficients. II
title_sort center manifold method in the asymptotic integration problem for functional differential equations with oscillatory decreasing coefficients ii
topic functional-differential equations
critical manifold
asymptotic integration
averaging method
levinson’s theorem
url https://www.mais-journal.ru/jour/article/view/82
work_keys_str_mv AT pnnesterov centermanifoldmethodintheasymptoticintegrationproblemforfunctionaldifferentialequationswithoscillatorydecreasingcoefficientsii