Linearized instability for nonlinear Schr?odinger and Klein-Gordon equations
Linearized instability for nonlinear Schr?odinger and Klein-Gordon equations
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非线性薛定谔和克莱因-戈登方程的线性不稳定性
DOI：
10.1002/cpa.3160410602
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Grillakis
中科院分区：
文献类型：
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作者：
M. Grillakis
在本文中，我介绍了一种新的技术证明束缚态的不稳定性的哈密顿系统。在文献中已经有两种不同类型的不稳定性结果。由Strauss-Shatah [20]开发的方法给出了来自问题的变分结构的不稳定性准则;另一方面，Jones的方法[11]使用完全不同的技术产生了与两个自伴算子的负特征值的数量之间的差异有关的补充准则。事实证明，本文中开发的方法，这两个标准可以在一个单一的框架内，也导致了以前的结果的推广。最后，为了说明这种方法是如何工作的，我在一些具体的例子中应用的不稳定性准则。
In this paper I am introducing a new technique for proving instability of bound states for Hamiltonian systems. There are already two disparate types of instability results in the literature. The approach developed by Strauss-Shatah [20] gave an instability criterion coming from the variational structure of the problem; on the other hand, Jones' approach [11] produced a complementary criterion related to the difference between the number of negative eigenvalues of two selfadjoint operators using quite different techniques. It turns out that with the methods developed in this paper these two criteria can be derived within a single framework that also leads to a generalization of the previous results. Finally in order to demonstrate how this method works I apply the instability criterion in some specific examples.