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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Seifedine Kadry & Gennady Alferov & Gennady Ivanov & Vladimir Korolev & Ekaterina Selitskaya, 2019. "A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:677-:d:252819
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    Citations

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    Cited by:

    1. Yuanyuan Tian & Jing Li, 2019. "Periodic Solutions for a Four-Dimensional Coupled Polynomial System with N-Degree Homogeneous Nonlinearities," Mathematics, MDPI, vol. 7(12), pages 1-21, December.
    2. Jing Li & Yuying Chen & Shaotao Zhu, 2022. "Periodic Solutions and Stability Analysis for Two-Coupled-Oscillator Structure in Optics of Chiral Molecules," Mathematics, MDPI, vol. 10(11), pages 1-24, June.

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