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Research Article | Open Access

Periodic solutions in reversible systems in second order systems with distributed delays

Yameng Duan1, Wieslaw Krawcewicz2, Huafeng Xiao1( )
School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
Department of Mathematical Sciences, the University of Texas at Dallas, Richardson, TX, 75080-3021, USA
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Abstract

In this paper, we study the existence and multiplicity of periodic solutions to a class of second-order nonlinear differential equations with distributed delay. Under assumptions that the nonlinearity is odd, differentiable at zero and satisfies the Nagumo condition, by applying the equivariant degree method, we prove that the delay equation admits multiple periodic solutions. The results are then illustrated by an example.

Keywords

delay differential systemdistributed delayequivariant degreeperiodic solutions
CLC number: 34K13, 58E05

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 8461-8475
DOI: 10.3934/math.2024411

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Cite this article:
Duan Y, Krawcewicz W, Xiao H. Periodic solutions in reversible systems in second order systems with distributed delays. AIMS Mathematics, 2024, 9(4): 8461-8475. https://doi.org/10.3934/math.2024411

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Received: 20 October 2023
Revised: 29 November 2023
Accepted: 20 December 2023
Published: 15 April 2024
©2024 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)