Applied problems of perturbation theory
Автор: Akmatov Abdilaziz, Toktorbaev Aibek, Zamirbek Kyzy Nargiza
Журнал: Бюллетень науки и практики @bulletennauki
Рубрика: Физико-математические науки
Статья в выпуске: 12 т.8, 2022 года.
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In this paper, we study solutions to nonlinear singularly perturbed differential equations with initial conditions. Proving the asymptotic closeness of the solutions of the perturbed and unperturbed problems on the real axis is a top-priority task. But it doesn't always work out. For the first time in works in this direction, the concept of bistability of solutions was introduced. The definition of stability to the right and to the left is given. As well as definitions of bistability of solutions. Examples are given. If the solution is bistable, then it is always possible to show the asymptotic closeness of the solutions of the perturbed and unperturbed problems on the real domain.
Bistability, contradiction method, majorant method, solutions, successive approximations, differential equations, newton's second law
Короткий адрес: https://sciup.org/14126022
IDR: 14126022 | DOI: 10.33619/2414-2948/85/04