Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities

Shuang Wang; Chunlian Liu; Shuang Wang; Chunlian Liu

doi:10.3934/era.2023182

Electronic Research Archive

2023, Volume 31, Issue 6: 3594-3608. doi: 10.3934/era.2023182

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Research article

Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities

Shuang Wang ¹,
Chunlian Liu ^{2
,
,}

1.
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224051, China
2.
School of Science, Nantong University, Nantong 226019, China

Received: 06 March 2023 Revised: 05 April 2023 Accepted: 14 April 2023 Published: 24 April 2023

We prove the existence of multiple periodic solutions for weakly coupled parametrized systems with a singularity of repulsive type at the origin and linear growth at infinity. The proof is based on a higher dimensional Poincaré-Birkhoff theorem and the phase-plane analysis of the solutions.
- periodic solutions,
- weakly coupled systems,
- systems with singularities,
- Poincaré-Birkhoff theorem
Citation: Shuang Wang, Chunlian Liu. Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities[J]. Electronic Research Archive, 2023, 31(6): 3594-3608. doi: 10.3934/era.2023182

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Abstract

We prove the existence of multiple periodic solutions for weakly coupled parametrized systems with a singularity of repulsive type at the origin and linear growth at infinity. The proof is based on a higher dimensional Poincaré-Birkhoff theorem and the phase-plane analysis of the solutions.

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