Nonlinear oscillators at resonance with periodic forcing
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911323938357248 |
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| author | Korman, Philip Li, Yi |
| author_facet | Korman, Philip Li, Yi |
| contents | In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of nonlinear equations with linear part at resonance and periodic forcing. We give conditions for the existence and non-existence of periodic solutions, and obtain a rather detailed description of the dynamics for nonlinear oscillations at resonance, in case periodic solutions do not exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear oscillators at resonance with periodic forcing Korman, Philip Li, Yi Dynamical Systems Mathematical Physics Analysis of PDEs Classical Analysis and ODEs In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of nonlinear equations with linear part at resonance and periodic forcing. We give conditions for the existence and non-existence of periodic solutions, and obtain a rather detailed description of the dynamics for nonlinear oscillations at resonance, in case periodic solutions do not exist. |
| title | Nonlinear oscillators at resonance with periodic forcing |
| topic | Dynamical Systems Mathematical Physics Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2512.14940 |