聊城大学学报（自然科学版）2025，Vol.38Issue(5)：663-668,6.DOI:10.19728/j.issn1672-6634.2025020013
具有周期位势的非线性阻尼振动系统周期解的存在性研究
Study on the existence of periodic solutions for nonlinear damped vibration systems with periodic potential
摘要
Abstract
Nonlinear damping vibration system is an important type of nonlinear system,widely appearing in control systems,circuit systems,mechanical systems and other engineering disciplines in nonlinear dy-namic systems.The existence of periodic solutions has a significant impact on the stability and control de-sign of the system.In this paper,the second-order nonlinear damping vibration system with periodic po-tential in N dimensional state space is studied.Firstly,the minimax principle is used to obtain that the nonlinear damping system has at least N+1 geometrically distinct periodic solutions.Then,when the pe-riodic solutions of the system are all non degenerate,the Morse theory is used to analyze the topological structure of the system and infer that the number of geometrically distinct periodic solutions is at least 2N.关键词
非线性阻尼振动系统/周期解/变分法/Morse理论Key words
nonlinear damped vibration system/periodic solution/variational methods/Morse theory分类
数理科学引用本文复制引用
张子涵,刘广刚..具有周期位势的非线性阻尼振动系统周期解的存在性研究[J].聊城大学学报（自然科学版）,2025,38(5):663-668,6.基金项目
国家自然科学基金项目(11901270) （11901270）
山东省自然科学基金项目(ZR2019BA019)资助 （ZR2019BA019）
