Nonlinear integrodifferential boundary value problems with deviating argument unsolved with respect to the derivative

• Дата: 2022
• Автори: Boichuk, O. A., Chuiko, S. M., Kuzmina, V. O., Бойчук, О. А., Чуйко, С. М., Кузьміна, В. О., Чуйко, Сергій Михайлович
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2022
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/6707
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 The investigations of  linear differential-algebraic boundary-value problems are closely connected with numerous applications of the corresponding mathematical models in the theory of nonlinear oscillations, mechanics, biology, radio-engineering, and the theory of stability of motion. Thus, the  problem of generalization of the results obtained by  S. Campbell, A. M. Samoilenko and O. A. Boichuk to the case of nonlinear boundary-value problems  unsolved with respect to the derivative seems to be quite urgent.  In particular, this is true for finding  necessary and sufficient conditions for the existence of the required solutions of  nonlinear integrodifferential boundary-value problems with deviating argument unsolved with respect to the derivative.  We establish the conditions for existence and propose a constructive scheme for finding the solutions of a nonlinear integrodifferential boundary-value problem with deviating argument unsolved with respect to the derivative.