Electron. J. Diff. Eqns., Vol. 2003(2003), No. 96, pp. 1-24.
### Large energy simple modes for a class of Kirchhoff equations

Marina Ghisi

**Abstract:**

It is well known that the Kirchhoff equation admits infinitely many
simple modes, i.e., time periodic solutions with only one Fourier
component in the space variable(s). We prove that for some form of
the nonlinear term these simple modes are stable provided that
their energy is large enough. Here stable means orbitally stable
as solutions of the two-modes system obtained considering initial
data with two Fourier components.
Submitted April 28, 2003. Published September 17, 2003.

Math Subject Classifications: 35L70, 37J40, 70H08.

Key Words: Kirchhoff equations, orbital stability, Hamiltonian systems,
Poincare map, KAM theory.

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Marina Ghisi

Dipartimento di Matematica

Universita degli Studi di Pisa

via M. Buonarroti 2, 56127 Pisa, Italy

email: ghisi@dm.unipi.it

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