Global determination of a nonlinearity from a periodic motion
Global determination of a nonlinearity from a periodic motion
复制标题
DOI：
10.1016/j.jmaa.2013.02.044
复制
发表时间：
2013-07
影响因子：
1.3
通讯作者：
Yutaka Kamimura;Takeshi Kaneya
中科院分区：
文献类型：
--
作者：
Yutaka Kamimura;Takeshi Kaneya
我们考虑一个由周期函数确定自治微分方程的非线性问题，即周期与振幅的关系。在假设函数为Lipschitz连续的条件下，建立了实现给定周期函数的非线性的整体存在性和表征。给出了非线性自主振动经典逆问题的一个全局解。我们还考虑了从零速度下周期与初始位置的关系中确定非线性的相关问题，并给出了非线性唯一的判据。这个结果适用于一个逆分岔问题。
We consider a problem of determining a nonlinearity of an autonomous differential equation from a period function, namely, a relation between periods and amplitudes. A global existence and a characterization of nonlinearities realizing a prescribed period function are established under the assumption that the function is Lipschitz continuous. This gives a global answer to a classical inverse problem in a nonlinear autonomous oscillation. We also consider a related problem of determining a nonlinearity from a relation between periods and initial positions with zero velocity, and give a criterion for the nonlinearity to be unique. This result applies to an inverse bifurcation problem.