On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type
Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type \(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\...
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| Дата: | 1992 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1992
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8032 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512876129681408 |
|---|---|
| author | Ivanov , A. F. Marushiyak , P. Иванов , А. Ф. Марушияк , П. |
| author_facet | Ivanov , A. F. Marushiyak , P. Иванов , А. Ф. Марушияк , П. |
| author_sort | Ivanov , A. F. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-12-28T09:25:14Z |
| description | Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type
\(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)),  \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1. \) |
| first_indexed | 2026-03-24T03:35:45Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-8032 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:35:45Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/9d/5de79ad40a1962d42f9120b32ca29d9d.pdf |
| spelling | umjimathkievua-article-80322023-12-28T09:25:14Z On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type Об осцилляции и асимптотическом поведении решений одной системы дифференциально-функциональных уравнений нейтрального типа Ivanov , A. F. Marushiyak , P. Иванов , А. Ф. Марушияк , П. Conditions for the oscillation of all solutions and for the existence of nonoscillatory solutions with polynomial growth at infinity are given for the system of differential-functional equations of neutral type \(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)),  \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1. \) Приводятся условия осцилляции всех решений и наличия неосцилирующих решений с полиномиальным ростом на бесконечности для системы дифференциально-функциональных уравнений нейтрального типа \(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)),  \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1. \) Наведено умови осциляції всіх розв'язків та існування неосцилюючих розв'язків з поліноміальним зростом на нескінченності для системи диференціально-функціональних рівнянь нейтрального типу \(\frac{{d^n }}{{dt^n }}[x(t) + \lambda _1 x(t - \tau _1 )] = p(t)f(y(\theta _1 (f)), \\ \frac{{d^n }}{{dt^n }}[y(t) + \lambda _2 y(t - \tau _2 )]q = (t)g(x(\theta _2 (t)),  \\ 0 \leqslant |\lambda _1 |,|\lambda _2 |< 1. \) Institute of Mathematics, NAS of Ukraine 1992-09-08 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8032 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 8 (1992); 1044-1049 Український математичний журнал; Том 44 № 8 (1992); 1044-1049 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8032/9595 Copyright (c) 1992 A. F. Ivanov , P. Marushiyak |
| spellingShingle | Ivanov , A. F. Marushiyak , P. Иванов , А. Ф. Марушияк , П. On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title | On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title_alt | Об осцилляции и асимптотическом поведении решений одной системы дифференциально-функциональных уравнений нейтрального типа |
| title_full | On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title_fullStr | On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title_full_unstemmed | On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title_short | On oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| title_sort | on oscilation and asymptotic behaviour of solutions of one system of differential-functional equations of neutral type |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8032 |
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