## Stability theory for solitary-wave solutions of scalar field equations.(English)Zbl 0546.35062

The authors study the stability of special travelling-wave (solitary- wave) solutions of classical scalar field equations of the form (1) $$\square\phi +u'(\phi)=0$$. They prove a stability result for a certain class of solutions of (1) under some assumptions on u. Furthermore they give a general instability result for fixed points of some nonlinear maps in a Banach space. Some applications of both theorems are discussed.
Reviewer: N.Jacob

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 35B35 Stability in context of PDEs 47H10 Fixed-point theorems
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### References:

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