### Ground state solutions for a class of nonlinear Maxwell-Dirac system

DOI: http://dx.doi.org/10.12775/TMNA.2015.068

#### Abstract

\begin{equation*}

\begin{cases}

\displaystyle

-i\sum^{3}_{k=1}\alpha_{k}\partial_{k}u + a\beta u + \omega u-\phi u =F_{u}(x,u),

\\

-\Delta \phi=4\pi|u|^{2,\\

\end{cases}

\end{equation*}

for $x\in\R^{3}$. The Dirac operator is unbounded from below and above, so the associated energy functional is strongly indefinite. We use the linking and concentration compactness arguments to establish the existence of ground state solutions

for this system with asymptotically quadratic nonlinearity.

#### Keywords

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