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Multiple solutions for superlinear elliptic systems of Hamiltonian type

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  • This paper is concerned with the following periodic Hamiltonian elliptic system

    $\-\Delta \varphi+V(x)\varphi=G_\psi(x,\varphi,\psi)$ in $\mathbb{R}^N,$
    $\-\Delta \psi+V(x)\psi=G_\varphi(x,\varphi,\psi)$ in $\mathbb{R}^N,$
    $\varphi(x)\to 0$ and $\psi(x)\to0$ as $|x|\to\infty.$

    Assuming the potential $V$ is periodic and $0$ lies in a gap of $\sigma(-\Delta+V)$, $G(x,\eta)$ is periodic in $x$ and superquadratic in $\eta=(\varphi,\psi)$, existence and multiplicity of solutions are obtained via variational approach.
    Mathematics Subject Classification: Primary: 35J50; Secondary: 35J55.


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