Existence results for solutions to nonlinear Dirac equations on compact spin manifolds |
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Authors: | Takeshi Isobe |
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Institution: | 1. Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo, 152-8551, Japan
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Abstract: | We consider super-linear and sub-linear nonlinear Dirac equations on compact spin manifolds. Their solutions are obtained as critical points of certain strongly indefinite functionals on a Hilbert space. For both cases, we establish existence results via Galerkin type approximations and linking arguments. For a particular case of odd nonlinearities, we prove the existence of infinitely many solutions. |
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