Nontrivial Solutions of Dirac-Laplace Equation on Compact Spin Manifolds

2022/01/23 by Xu Yang, Yang, Xu, Lei Xian +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2201.09311

openalex publication_date 2022/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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