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

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-07-22 DOI:10.1007/s12346-024-01101-0

Yuanhao Wang, Zihan Zhang, Guanggang Liu

引用次数: 0

Abstract

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.

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具有无穷大共振的一类渐近线性阻尼振动问题的周期解

在本文中，我们考虑了一类在无穷远处存在共振的渐近线性阻尼振动问题。与现有结果相比，在这种共振条件下，问题对应的函数可能不满足紧凑性条件。通过结合惩罚函数技术、莫尔斯理论和两个临界点定理，我们得到了非微观周期解的存在性和多重性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.