Nontrivial Solutions of Dirac-Laplace Equation on Compact Spin Manifolds

Xu Yang; Lei Xian

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arXiv · 2201.09311

Nontrivial Solutions of Dirac-Laplace Equation on Compact Spin Manifolds

Xu Yang·Lei Xian

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Abstract

We apply the Fountain theorem to a class of nonlinear Dirac-Laplace equation on compact spin manifold. We show the standard Ambrosetti-Rabinowitz condition can be replaced by a more natural super-quadratic condition that is enough to obtain the Cerami condition under certain conditions. Multiple solutions of nonlinear Dirac-Laplace equation are obtained in this note.

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Xu Yang, Lei Xian. 2022-01-23. Nontrivial Solutions of Dirac-Laplace Equation on Compact Spin Manifolds. https://arxiv.org/abs/2201.09311

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