Continuous dependence and estimates of eigenvalues for periodic generalized Camassa-Holm equations
Continuous dependence and estimates of eigenvalues for periodic generalized Camassa-Holm equations
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DOI：
10.1016/j.jde.2020.04.042
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发表时间：
2020-09
影响因子：
2.4
通讯作者：
Jifeng Chu;Gang Meng;Zhi Zhang
中科院分区：
文献类型：
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作者：
Jifeng Chu;Gang Meng;Zhi Zhang
研究周期广义Camassa-Holm方程的谱问题（y1 y2）x=（− 1 2 1 2 λ m− 1 2 λ m1 2）（y1 y2）.第一个目的是研究特征值的结构，证明特征值对势函数的连续依赖性。证明了在Lebesgue空间L1 [0，T]中，作为势的非线性泛函，特征值在关于弱拓扑的势中是连续的.第二个目的是在势函数的L1范数给定的情况下，利用迹公式的应用，得到特征值的估计。
In this paper we are concerned with the spectral problem (y 1 y 2) x=(− 1 2 1 2 λ m− 1 2 λ m 1 2)(y 1 y 2) for the periodic generalized Camassa-Holm equations. The first aim is to study the structure of eigenvalues and prove the continuous dependence of eigenvalues on potentials. We prove that as nonlinear functionals of potentials, eigenvalues are continuous in potentials with respect to the weak topologies in the Lebesgue space L 1 [0, T]. The second aim is to find the estimates of the eigenvalues when the L 1 norm of potentials is given, based on an application of trace formulas.