The existence of time periodic solutions of nonlinear wave equations
on -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 and the non-symmetric perturbation 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
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