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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Isobe, T. Existence results for solutions to nonlinear Dirac equations on compact spin manifolds. manuscripta math. 135, 329–360 (2011). https://doi.org/10.1007/s00229-010-0417-6
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DOI: https://doi.org/10.1007/s00229-010-0417-6