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Strong instability of standing waves for nonlinear Klein-Gordon equations. (English) Zbl 1065.35198
Summary: The strong instability of ground state standing wave solutions \(e^{i\omega t}\varphi_\omega(x)\) for nonlinear Klein-Gordon equations \[ \partial^2_tu-\Delta u+u=|u|^{p-1}u,\quad (t,x)\in\mathbb{R} \times\mathbb{R}^n, \] has been known only for the case \(\omega=0\). In this paper we prove the strong instability for small frequency \(\omega\).

MSC:
35L70 Second-order nonlinear hyperbolic equations
35B35 Stability in context of PDEs
35A15 Variational methods applied to PDEs
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