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.