具有Soler型非线性项的非线性Dirac方程的周期解
Periodic Solutions for a Nonlinear Dirac Equation with Soler-Type Nonlinearity
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中文总结 AI 辅助
针对三维环面上带Soler型非线性的非线性Dirac方程，通过引入强制扰动恢复Palais–Smale条件，结合谱估计与联结论证，证明了质量以下区间内任意谱参数对应的非平凡连续可微周期解存在性。
中文摘要 AI 辅助
我们研究三维环面上具有次临界Soler型非线性项的非线性Dirac方程。该变分问题是强不定的，而非强制的Soler势阻碍了直接紧性。我们通过引入小的强制扰动恢复Palais–Smale条件。精细谱估计和联结论证给出具有一致能量界的扰动解。当扰动消失时取极限，得到非平凡的连续可微周期解。该存在性结果对质量以下显式区间内的每个谱参数都成立。
英文摘要
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.
