The existence of periodic solutions for nonconservative superlinear second order ODEs: a rotation number and spiral analysis approach

We investigate the existence of periodic solutions for nonconservative superlinear second-order differential equations in the sense of rotation numbers. Specifically, we focus on equations whose solutions at infinity behave comparably to a suitable linear system. By employing a rotation number appro...

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Bibliographic Details
Main Authors: Shuang Wang, FanFan Chen, Chunlian Liu
Format: Article
Language:English
Published: AIMS Press 2025-01-01
Series:Electronic Research Archive
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Online Access:https://www.aimspress.com/article/doi/10.3934/era.2025003
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Summary:We investigate the existence of periodic solutions for nonconservative superlinear second-order differential equations in the sense of rotation numbers. Specifically, we focus on equations whose solutions at infinity behave comparably to a suitable linear system. By employing a rotation number approach, spiral analysis, and fixed-point theorems, we establish the existence of periodic solutions for nonconservative superlinear second-order differential equations. Among the equations we consider, a notable subclass is partially superlinear second-order differential equations, which provide a concrete illustration of our results. Our results extend several recent results, thereby advancing to a more comprehensive understanding of periodic behavior in nonconservative systems.
ISSN:2688-1594