Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 95-105.

Infinitely many periodic solutions of nonlinear wave equations on $S^n$

Jintae Kim

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.

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Jintae Kim
Department of Mathematics, Tuskegee University
Tuskegee, AL 36088, USA
email: jtkim@tuskegee.edu

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