Instability for standing waves of nonlinear Klein-Gordon equations via mountain-pass arguments
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- by Louis Jeanjean and Stefan Le Coz PDF
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Abstract:
We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital stability/instability. For a power-type nonlinearity, we prove that the ground states of the associated stationary equation are minimizers of the functional action on a wide variety of constraints. For a general nonlinearity, we extend to the dimension $N=2$ the classical instability result for stationary solutions of nonlinear Klein-Gordon equations proved in 1985 by Shatah in dimension $N\geqslant 3$.References
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Additional Information
- Louis Jeanjean
- Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
- MR Author ID: 318795
- Email: louis.jeanjean@univ-fcomte.fr
- Stefan Le Coz
- Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France
- Address at time of publication: Department of Mathematics, Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014 Trieste, Italy
- Email: slecoz@univ-fcomte.fr, lecoz@sissa.it
- Received by editor(s): October 16, 2007
- Published electronically: May 11, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 5401-5416
- MSC (2000): Primary 35Q53, 35B35, 35A15, 35Q51
- DOI: https://doi.org/10.1090/S0002-9947-09-04790-4
- MathSciNet review: 2515816