Multiplicity of periodic solutions for weakly coupled parametrized systems with singularities

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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Bibliographic Details
Published in:Electronic research archive 2023-01, Vol.31 (6), p.3594-3608
Main Authors: Wang, Shuang, Liu, Chunlian
Format: Article
Language:English
Subjects:
periodic solutions
poincaré-birkhoff theorem
systems with singularities
weakly coupled systems
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Description
Summary: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.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2023182