Seventh Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 17 (2009), pp. 95-105.
Title: Infinitely many periodic solutions of nonlinear wave equations on $S^n$
Author: Jintae Kim (Tuskegee Univ., Tuskegee, AL 36088, USA)
Abstract:
The existence of time periodic solutions of nonlinear
wave equations
$$
u_{tt} - \Delta_n u + \big(\frac{n-1}{2}\big)^2u= g(u) - f(t, x)
$$
on $n$-dimensional spheres is considered. The corresponding
functional of the equation is studied by the convexity in
suitable subspaces, minimax arguments for almost symmetric
functional, comparison principles and Morse theory.
The existence of infinitely many time periodic solutions is
obtained where $g(u)= |u|^{p-2}u$ and the non-symmetric
perturbation $f$ is not small.
Published April 15, 2009.
Math Subject Classifications: 20H15, 20F18, 20E99, 53C55.
Key Words: Minimax theory; Morse index; critical points.