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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-01-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| 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. |
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| ISSN: | 2688-1594 |