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

Seifedine Kadry, Gennady Alferov, Gennady Ivanov, Vladimir Korolev and Ekaterina Selitskaya
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Seifedine Kadry: Department of mathematics and computer science, faculty of science, Beirut Arab University, P.O. Box 11-5020 Riad El Solh, Beirut 1107 2809, Lebanon
Gennady Alferov: Faculty of Applied Mathematics and Control Processes, Sain-Petersburg State University, 199034 Saint-Petersburg, Russia
Gennady Ivanov: Faculty of Applied Mathematics and Control Processes, Sain-Petersburg State University, 199034 Saint-Petersburg, Russia
Vladimir Korolev: Faculty of Applied Mathematics and Control Processes, Sain-Petersburg State University, 199034 Saint-Petersburg, Russia
Ekaterina Selitskaya: Faculty of Applied Mathematics and Control Processes, Sain-Petersburg State University, 199034 Saint-Petersburg, Russia

Mathematics, 2019, vol. 7, issue 8, 1-15

Abstract: 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.

Keywords: derived number; periodic solutions; Non-smooth analysis; Dini-Holder derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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