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Research Article | Open Access

Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities

Shuang Wang1, Chunlian Liu2( )
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224051, China
School of Science, Nantong University, Nantong 226019, China
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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.

Keywords

periodic solutionsweakly coupled systemssystems with singularitiesPoincaré-Birkhoff theorem

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Electronic Research Archive
Volume 31 Issue 6,
June 2023
Pages 3594-3608
DOI: 10.3934/era.2023182

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Cite this article:
Wang S, Liu C. Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities. Electronic Research Archive, 2023, 31(6): 3594-3608. https://doi.org/10.3934/era.2023182

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Received: 06 March 2023
Revised: 05 April 2023
Accepted: 14 April 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

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