Ground state solutions for a class of nonlinear Maxwell-Dirac system
DOI:
https://doi.org/10.12775/TMNA.2015.068Słowa kluczowe
Maxwell-Dirac system, Ground state solutions, Asymptotically quadratic, Strongly indefinite functionalsAbstrakt
This paper is concerned with the following nonlinear Maxwell-Dirac system\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.
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