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...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2014-10-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/82 |
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| _version_ | 1849338719400624128 |
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| 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 |