
Minimax Theory and its Applications 07 (2022), No. 2, 253276 Copyright Heldermann Verlag 2022 Nonrelativistic Limit of Ground State Solutions for Nonlinear DiracKleinGordon Systems Xiaojing Dong School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, P. R. China dongxj@bnu.edu.cn Zhongwei Tang School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University, P. R. China tangzw@bnu.edu.cn [Abstractpdf] We study the nonrelativistic limit and some properties of the solutions\\[1.5mm] \centerline{$(\psi, \phi) := (u, v,\phi)\in \mathbb{C}^2\times\mathbb{C}^2\times \mathbb{R}$}\\[1.5mm] for the following nonlinear DiracKleinGordon systems: \begin{equation*} \left\{ \begin{aligned} & ic \sum_{k=1}^3 \alpha_k \partial_k \psi  m c^2 \beta \psi  \omega \psi\lambda \phi\beta \psi =\psi^{p2}\psi, \\ & \Delta \phi+c^2M^2 \phi=4 \pi \lambda(\beta \psi) \cdot\psi, \end{aligned}\right. \end{equation*} where $p \in [\frac{12}{5},\frac{8}{3}],$ $c$ denotes the speed of light, $m > 0$ is the mass of the electron. We show that the first component $u$ and the last one $\phi$ of ground state solutions for nonlinear DiracKleinGordon systems converge to zero and the second one $v$ converges to corresponding solutions of a coupled system of nonlinear Schr\"{o}dinger equations as the speed of light tends to infinity for electrons with small mass. Moreover, we also prove the uniform boundedness and the exponential decay properties of the solutions for the nonlinear DiracKleinGordon systems with respect to the speed of light $c$. Keywords: Nonlinear DiracKleinGordon systems, nonrelativistic limit, ground state solution. MSC: 35Q40, 49J35. [ Fulltextpdf (193 KB)] for subscribers only. 