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Research Article | Open Access

Periodic solutions and limit cycles of mixed Lienard-type differential equations

K. K. D. Adjaï, J. Akande, A. V. R. Yehossou, M. D. Monsia( )
Department of Physics, University of Abomey-Calavi, Abomey-Calavi, 01.BP.526, Cotonou, Benin
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Abstract

In the attractive research field of nonlinear differential equations, there are a few studies devoted to finding exact and explicit harmonic and isochronous periodic solutions and limit cycles. In this contribution, we present some classes of polynomial mixed Lienard-type differential equations that can generate many equations with exact solutions. These classes of equations constitute counterexamples of the classical existence theorems.

Keywords

polynomial mixed Lienard-type differential equationsexact harmonic and isochronous periodic solutionsexact algebraic limit cyclesclassical existence theorems
CLC number: 34A05, 34C05, 34C25, 34C15

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 15195-15211
DOI: 10.3934/math.2022833

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Cite this article:
Adjaï KKD, Akande J, Yehossou AVR, et al. Periodic solutions and limit cycles of mixed Lienard-type differential equations. AIMS Mathematics, 2022, 7(8): 15195-15211. https://doi.org/10.3934/math.2022833

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Received: 29 March 2022
Revised: 25 May 2022
Accepted: 02 June 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)