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 |
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| 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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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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| DOI: | 10.37863/umzh.v74i11.6083 |