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Pure Mathematics 2025
变系数非线性梁方程的周期解
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Abstract:
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。
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.
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