Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 96, pp. 1-24.
Title: Large energy simple modes for a class of Kirchhoff equations
Author: Marina Ghisi (Univ. degli Studi di Pisa, Italy)
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.