Periodic solutions for a class of asymptotically linear damped vibration problems with resonance at infinity

In this paper, we consider a class of asymptotically linear damped vibration problems with resonance at infinity. Compared with the existing results, under this resonance condition the functional corresponding to the problem may not satisfy the compactness condition. By combining the penalized funct...

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Bibliographic Details
Published in:	Qualitative theory of dynamical systems Vol. 23; no. 5
Main Authors:	Wang, Yuanhao, Zhang, Zihan, Liu, Guanggang
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-11-2024 Springer Nature B.V
Subjects:	Critical point Difference and Functional Equations Dynamical Systems and Ergodic Theory Infinity Mathematics Mathematics and Statistics Resonance Vibration Morse theory 35J50 Periodic solutions 35J60 35J57 Damped vibration problems
Online Access:	Get full text
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Summary:	In this paper, we consider a class of asymptotically linear damped vibration problems with resonance at infinity. Compared with the existing results, under this resonance condition the functional corresponding to the problem may not satisfy the compactness condition. By combining the penalized functional technique, Morse theory and two critical point theorems, we obtain the existence and multiplicity of nontrivial periodic solutions.
ISSN:	1575-5460 1662-3592
DOI:	10.1007/s12346-024-01101-0