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Article

A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

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Department of mathematics and computer science, faculty of science, Beirut Arab University, P.O. Box 11-5020 Riad El Solh, Beirut 1107 2809, Lebanon
2
Faculty of Applied Mathematics and Control Processes, Sain-Petersburg State University, 199034 Saint-Petersburg, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 677; https://doi.org/10.3390/math7080677
Received: 5 July 2019 / Revised: 24 July 2019 / Accepted: 24 July 2019 / Published: 29 July 2019
In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered. View Full-Text
Keywords: derived number; periodic solutions; Non-smooth analysis; Dini-Holder derivatives derived number; periodic solutions; Non-smooth analysis; Dini-Holder derivatives
MDPI and ACS Style

Kadry, S.; Alferov, G.; Ivanov, G.; Korolev, V.; Selitskaya, E. A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis. Mathematics 2019, 7, 677. https://doi.org/10.3390/math7080677

AMA Style

Kadry S, Alferov G, Ivanov G, Korolev V, Selitskaya E. A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis. Mathematics. 2019; 7(8):677. https://doi.org/10.3390/math7080677

Chicago/Turabian Style

Kadry, Seifedine, Gennady Alferov, Gennady Ivanov, Vladimir Korolev, and Ekaterina Selitskaya. 2019. "A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis" Mathematics 7, no. 8: 677. https://doi.org/10.3390/math7080677

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