We consider a Hamiltonian systems 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.
- Bound states
- Nonlinear Klein-Gordon equation
- Nonlinear Schrödinger equation
- Orbital stability
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