非线性Euler-Bernoulli梁方程的周期解
Periodic Solutions to Nonlinear Euler-Bernoulli Beam Equations
摘要：
薄梁和薄板的弯曲振动可以用非线性Euler-Bernoulli梁方程描述，方程中的系数与$x$有关。本文利用Lyapunov-Schmidt约化和可微Nash-Moser迭代方法研究了这类模型的时间周期解族的存在性。结果适用于康托尔集的所有参数$(ε,ω)$，其渐近满测度为$ε\rightarrow0$。
英文摘要：
Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using Lyapunov-Schmidt reduction and a differentiable Nash-Moser iteration scheme. The results hold for all parameters $(ε,ω)$ in a Cantor set with asymptotically full measure as $ε\rightarrow0$.
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