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Stability of bound states of Hamiltonian PDEs in the degenerate cases. (English) Zbl 1244.35008

Summary: We consider a Hamiltonian system which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.

MSC:

35B35 Stability in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q40 PDEs in connection with quantum mechanics
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