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On coupled Dirac systems

  • * Corresponding author: Wenmin Gong

    * Corresponding author: Wenmin Gong 

The first author is supported by the NSF (grant no. 11571194) of China.
The second author is Partially supported by the NNSF (grant no. 10971014 and 11271044) of China.

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  • In this paper, we show the existence of solutions for the coupled Dirac system

    where $M$ is an $n$-dimensional compact Riemannian spin manifold, $D$ is the Dirac operator on $M$, and $H:\Sigma M\oplus \Sigma M\to \mathbb{R}$ is a real valued superquadratic function of class $C^1$ in the fiber direction with subcritical growth rates. Our proof relies on a generalized linking theorem applied to a strongly indefinite functional on a product space of suitable fractional Sobolev spaces. Furthermore, we consider the $\mathbb{Z}_2$-invariant $H$ that includes a nonlinearity of the form


    where $f(x)$ and $g(x)$ are strictly positive continuous functions on $M$ and $p, q>1$ satisfy


    In this case we obtain infinitely many solutions of the coupled Dirac system by using a generalized fountain theorem.

    Mathematics Subject Classification: Primary: 53C27, 57R58, 58E05, 58J05.


    \begin{equation} \\ \end{equation}
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