New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique
UDC 517.9 A new mathematical model described by a Volterra integro-differential equation (VIDE) with constant delay is examined.  New agreeable conditions on the uniformly asymptotic stability, boundedness, and square integrability of solutions of the VIDE are obtained by u...
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| Дата: | 2026 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6083 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512262260785152 |
|---|---|
| author | Tunç, Osman Korkmaz, E. Tunç, Osman Korkmaz, E. |
| author_facet | Tunç, Osman Korkmaz, E. Tunç, Osman Korkmaz, E. |
| author_sort | Tunç, Osman |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-23T13:26:26Z |
| description | UDC 517.9
A new mathematical model described by a Volterra integro-differential equation (VIDE) with constant delay is examined.  New agreeable conditions on the uniformly asymptotic stability, boundedness, and square integrability of solutions of the VIDE are obtained by using the Lyapunov–Razumikhin technique.  The established conditions improve some former results and they are also nonlinear generalizations of these results.  Moreover, they are weaker than some  available results  cited in the bibliography of this paper.  Two examples are presented to demonstrate applications of these results and the  introduced concepts.  The use of the Lyapunov–Razumikhin technique leads to  a significant difference and gives an advantage over the related methods used in the books and papers cited in the bibliography. |
| doi_str_mv | 10.37863/umzh.v74i11.6083 |
| first_indexed | 2026-03-24T03:25:59Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-6083 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:25:59Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/61/2971633b3d4d8c211e4167bc73299361 |
| spelling | umjimathkievua-article-60832026-02-23T13:26:26Z New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique Tunç, Osman Korkmaz, E. Tunç, Osman Korkmaz, E. VIDDE, UAS, boundedness, square integrability, LRT, fixed constant delay. UDC 517.9 A new mathematical model described by a Volterra integro-differential equation (VIDE) with constant delay is examined.  New agreeable conditions on the uniformly asymptotic stability, boundedness, and square integrability of solutions of the VIDE are obtained by using the Lyapunov–Razumikhin technique.  The established conditions improve some former results and they are also nonlinear generalizations of these results.  Moreover, they are weaker than some  available results  cited in the bibliography of this paper.  Two examples are presented to demonstrate applications of these results and the  introduced concepts.  The use of the Lyapunov–Razumikhin technique leads to  a significant difference and gives an advantage over the related methods used in the books and papers cited in the bibliography. УДК 517.9 Нові результати з якісного аналізу розв'язків ІДРВ за методикою Ляпунова–Разуміхіна Розглянуто нову математичну модель, що описується інтегро-диференціальним рівнянням Вольтерра (ІДРВ) зі сталим запізненням.  За допомогою техніки Ляпунова–Разуміхіна отримано нові прийнятні умови рівномірно асимптотичної стійкості, обмеженості та квадратичної інтегровності розв'язків цього ІДРВ.  Встановлені умови покращують деякі попередні результати, а також є їх нелінійними узагальненнями.  Крім того, вони слабші, ніж деякі результати, доступні в бібліографії цієї статті.  Наведено два приклади, щоб продемонструвати можливе застосування цих результатів і введених концепцій.  Використання техніки Ляпунова–Разуміхіна приводить до значних відмінностей та надає певну перевагу порівняно з відповідними методами, що використовуються в книгах і статтях, наведених у бібліографії.  Institute of Mathematics, NAS of Ukraine 2026-02-22 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/6083 10.37863/umzh.v74i11.6083 Ukrains’kyi Matematychnyi Zhurnal; Vol. 74 No. 11 (2022); 1544 - 1557 Український математичний журнал; Том 74 № 11 (2022); 1544 - 1557 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6083/9333 Copyright (c) 2022 Osman Tunç, Erdal Korkmaz |
| spellingShingle | Tunç, Osman Korkmaz, E. Tunç, Osman Korkmaz, E. New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_alt | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_full | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_fullStr | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_full_unstemmed | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_short | New results on the qualitative analysis of solutions of VIDEs by the Lyapunov–Razumikhin technique |
| title_sort | new results on the qualitative analysis of solutions of vides by the lyapunov–razumikhin technique |
| topic_facet | VIDDE UAS boundedness square integrability LRT fixed constant delay. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6083 |
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