## Infinitely many solutions for a class of superlinear Dirac-Poisson system.(English)Zbl 1394.35391

Summary: This paper is concerned with the nonlinear Dirac-Poisson system $\begin{cases} -i \sum_{k = 1}^3 \alpha_k \partial_k u +(V(x) + a) \beta u + \omega u - \phi u = F_u(x,u), \\ -\varDelta \phi = 4 \pi |u|^2, \end{cases} \quad \text{in} \; \mathbb{R}^3$ where $$V$$ is an external potential and $$F$$ is a superlinear nonlinearity modeling various types of interactions. Existence and multiplicity of stationary solutions are obtained for the system with periodicity condition via variational methods.

### MSC:

 35Q41 Time-dependent Schrödinger equations and Dirac equations 35Q60 PDEs in connection with optics and electromagnetic theory 35A15 Variational methods applied to PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence
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### References:

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