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Linearized instability for nonlinear schrödinger and klein‐gordon equations
Author(s) -
Grillakis Manoussos
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410602
Subject(s) - instability , mathematics , eigenvalues and eigenvectors , generalization , nonlinear system , hamiltonian (control theory) , upper and lower bounds , mathematical analysis , mathematical optimization , physics , quantum mechanics
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.