Strong instability of standing waves for nonlinear Klein-Gordon equations

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February 2005, 12(2): 315-322. doi: 10.3934/dcds.2005.12.315

Strong instability of standing waves for nonlinear Klein-Gordon equations

Masahito Ohta ^1, and Grozdena Todorova ^2,

1.	Department of Mathematics, Faculty of Science, Saitama University, Japan
2.	Department of Mathematics, University of Tennessee, Knoxville, TN 37096-1300, United States

Received July 2003 Revised June 2004 Published December 2004

Abstract
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The strong instability of ground state standing wave solutions $e^{i\omega t}\phi_{\omega}(x)$ for nonlinear Klein-Gordon equations has been known only for the case $\omega=0$. In this paper we prove the strong instability for small frequency $\omega$.

Keywords: nonlinear Klein-Gordon equation., Stability/instability problems, blow-up, ground state standing waves.

Mathematics Subject Classification: 35L70, 35B35, 35A1.

Citation: Masahito Ohta, Grozdena Todorova. Strong instability of standing waves for nonlinear Klein-Gordon equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 315-322. doi: 10.3934/dcds.2005.12.315

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