Periodic Solutions for a Nonlinear Dirac Equation with Soler-Type Nonlinearity

Fuping Zhang

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arXiv · 2608.25320

Periodic Solutions for a Nonlinear Dirac Equation with Soler-Type Nonlinearity

Fuping Zhang

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Abstract

We study nonlinear Dirac equations on the three-dimensional torus with subcritical Soler-type nonlinearities. The variational problem is strongly indefinite, while the non-coercive Soler potential prevents direct compactness. We recover the Palais--Smale condition by introducing a small coercive perturbation. Refined spectral estimates and a linking argument yield perturbed solutions with uniform energy bounds. Passing to the limit as the perturbation vanishes gives a nontrivial continuously differentiable periodic solution. This existence result holds for every spectral parameter in an explicit interval below the mass.

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Fuping Zhang. 2026-08-26. Periodic Solutions for a Nonlinear Dirac Equation with Soler-Type Nonlinearity. https://arxiv.org/abs/2608.25320

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