Linearized instability for nonlinear schrödinger and klein‐gordon equations

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.