Study on the existence of periodic solutions for nonlinear damped vibration systems with periodic potential
ZHANG Zihan
LIU Guanggang
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.
Keywords：nonlinear damped vibration systemperiodic solutionvariational methodsMorse theory
Publication Date：2025-10-25
Online Publishing Date：2026-08-28(First online date of this platform, not the publication date of the document)
Pages：6( 663-668 )