%0 Journal Article
%T 变系数非线性梁方程的周期解<br>Periodic Solutions of Nonlinear Beam Equation with x-Dependent Coefficient
%A 陈俊毅
%A 马牧
%J Pure Mathematics
%P 25-32
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.152042
%X 本文考虑了具有空间变系数的非线性梁方程的边值问题&#65292;关注其时间周期解的存在性。通过推广Lyapunov中心定理&#65292;我们证明了当频率满足一个Diophantine型的非共振条件时&#65292;在系统的椭圆平衡点附近存在相同频率的时间周期轨。<br>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.
%K 非线性梁方程&#65292
%K 周期解&#65292
%K Lyapunov中心定理<br>Nonlinear Beam Equation
%K Periodic Solution
%K Lyapunov Center Theorem
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106864