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

Yameng Duan; Wieslaw Krawcewicz; Huafeng Xiao; Yameng Duan; Wieslaw Krawcewicz; Huafeng Xiao

doi:10.3934/math.2024411

AIMS Mathematics

2024, Volume 9, Issue 4: 8461-8475. doi: 10.3934/math.2024411

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

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
2.
Department of Mathematical Sciences, the University of Texas at Dallas, Richardson, TX, 75080-3021, USA

Received: 20 October 2023 Revised: 29 November 2023 Accepted: 20 December 2023 Published: 28 February 2024
MSC : 34K13, 58E05

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.
- delay differential system,
- distributed delay,
- equivariant degree,
- periodic solutions
Citation: Yameng Duan, Wieslaw Krawcewicz, Huafeng Xiao. Periodic solutions in reversible systems in second order systems with distributed delays[J]. AIMS Mathematics, 2024, 9(4): 8461-8475. doi: 10.3934/math.2024411

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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.

References

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