Email this article ON MINIMA OF FUNCTIONALS AND IMPLICIT DIFFERENTIAL EQUATIONS
- Authors: Zhukovskiy S.E.1
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Affiliations:
- RUDN University
- Issue: Vol 22, No 6 (2017)
- Pages: 1298-1303
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/362883
- DOI: https://doi.org/10.20310/1810-0198-2017-22-6-1298-1303
- ID: 362883
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Abstract
The stability of Caristi-like conditions under small Lipschitz perturbations is proved for functionals on metric spaces. The result obtained is used for the investigation of implicit differential equation. Sufficient conditions for solvability of Cauchy problem for implicit ordinary differential equations are obtained.
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About the authors
Sergey Evgenyevich Zhukovskiy
RUDN University
Email: s-e-zhuk@yandex.ru
Candidate of Physics and Mathematics, Associate Professor of the Nonlinear Analysis and Optimization Department 6 Miklukho-Maklay St., Moscow, Russian Federation, 117198
References
Арутюнов А.В. Условие Каристи и существование минимума ограниченной снизу функции в метрическом пространстве. Приложения к теории точек совпадения // Тр. МИАН. 2015. Т. 291. С. 30-44. Колмогоров А.Н., Фомин С.В. Элементы теории функций и функционального анализа. М.: Наука, 1976. Zabreiko P.P., Koshelev A.I., Krasnosel’skii M.A., et al. Integral Equations. M.: Nauka, 1968. Warga J. Optimal Control of Differential and Functional Equations. N.Y.: Academic Press, 1972.
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