arXiv subjects

Fuping Zhang

Publications and source records attributed to Fuping Zhang.

4 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

Stationary periodic solutions for nonlinear Dirac equations with non-coercive nonlinearity II: splitting

We study stationary periodic solutions of nonlinear Dirac equations with Soler-type nonlinearities. By splitting off a circle factor the problem is reduced to dimension two. The nonlinearity degenerates along a Lorentz null cone, causing difficulties for the variational analysis. Using a coercive perturbation we first obtain minimax perturbed solutions. The key new ingredient is a quantitative separation of the lowest positive eigenspace of the reduced Dirac operator from the null cone; together with a uniform resolvent estimate, it yields uniform bounds that allow us to remove the perturbation. This produces nontrivial periodic solutions for temporal frequencies near the corresponding positive spectral threshold, including frequencies above the mass.

math.AP↗

arXiv2026

Stationary periodic solutions to Nonlinear Dirac equations with non-coercive potentials

Motivated by the Soler model, we study a nonlinear Dirac equation with a non-coercive Soler-type nonlinearity. Stationary periodic solutions are obtained via variational methods. This amounts to studying the equation on a three-dimensional torus, where the spectrum of the physical Dirac operator on the torus needs to be clarified. To overcome the failure of coercivity of the potential we use a coercive perturbation. By carefully analyzing the critical levels and the linking structures, uniform estimates for the perturbed critical points are obtained when the frequency is sufficiently close to the mass. This allows us to pass to the zero-perturbation limit and obtain a nontrivial periodic solution.The argument also extends to suitable scalar external fields.

math.AP↗

arXiv2013

Genuine driving voltage on polarization fatigue in (Pb,La)(Zr,Ti)O3 antiferroelectric thin films

The polarization fatigue in (Pb0.97La0.02)(Zr0.95Ti0.05)O3 (PLZT) antiferroelectric thin films deposited onto silicon wafers is studied by investigating the effect of the peak/average/effective cycling voltage through varying the waveform of the electrical excitation. Interestingly, it is found that the fatigue endurance of the film is determined by the effective voltage of the external driving excitation rather than by the peak or average voltages. Our results can be well explained in the framework of the local phase decomposition model and indicate that the effective voltage should be considered as the genuine driving voltage determining the polarization fatigue in PLZT antiferroelectric films.

cond-mat.mtrl-sci↗