In this paper, we consider a nonlinear integro-vector differential equation of the second order. We establish sufficient conditions that guarantee the global existence and boundedness of solutions of the equation considered. The method of proof involves constructing a suitable Lyapunov functional that gives meaningful results for the problem to be investigated. The result obtained is new and complements that found in the literature. We give an example to verify the result obtained and for illustration purposes. Using MATLAB-Simulink, the behaviors of the orbits of the equation considered are clearly shown.
The purpose of this paper is to study the global existence and boundedness of solutions to a kind of nonlinear integro-differential equations of second order by integral inequalities. Some illustrative examples are also provided. Our results complement and improve some ones in the literature.
In this paper, we consider the global existence and boundedness of solutions for a certain nonlinear integro-differential equation of second order with multiple constant delays. We obtain some new sufficient conditions which guarantee the global existence and boundedness of solutions to the considered equation. The obtained result complements some recent ones in the literature. An example is given of the applicability of the obtained result. The main tool employed is an appropriate Lyapunov-Krasovskii type functional.
This paper considers a nonlinear integro-differential equation of third order with delay. We establish sufficient conditions which guarantee the globally existence and boundedness of the solutions of the equation considered. We benefit from the Lyapunov's second method to prove the main result. An example is also given to illustrate the applicability of our result. The result of this paper is new and improves previously known results.Вивчається нелiнiйне iнтегро-диференцiальне рiвняння третього порядку з запiзненням. Наведено достатнi умови глобального iснування та обмеженостi розв'язкiв розглянутих рiвнянь. Для доведення основного результату використовується другий метод Ляпунова. Також наведено приклад для iлюстрацiї отриманого результату. Отриманий результат є новим та покращує отриманi ранiше результати.
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