变系数非线性梁方程的周期解
Periodic Solutions of Nonlinear Beam Equation with x-Dependent Coefficient
DOI: 10.12677/pm.2025.152042, PDF,    国家自然科学基金支持
作者: 陈俊毅, 马 牧*：福州大学数学与统计学院，福建 福州
关键词: 非线性梁方程；周期解；Lyapunov中心定理；Nonlinear Beam Equation； Periodic Solution； Lyapunov Center Theorem
摘要: 本文考虑了具有空间变系数的非线性梁方程的边值问题，关注其时间周期解的存在性。通过推广Lyapunov中心定理，我们证明了当频率满足一个Diophantine型的非共振条件时，在系统的椭圆平衡点附近存在相同频率的时间周期轨。
Abstract: This paper is concerned with the time-periodic solutions of the boundary value problem of nonlinear beam equations with x-dependent coefficient. By introducing an infinite version of Lyapunov center theorem, we prove the existence of periodic orbits for frequencies satisfy a Diopantine condition.
文章引用：陈俊毅, 马牧. 变系数非线性梁方程的周期解[J]. 理论数学, 2025, 15(2): 25-32. https://doi.org/10.12677/pm.2025.152042

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