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A note on a superlinear and periodic elliptic system in the whole space

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

    $ -\Delta u+V(x)u=g(x,v)$ in $R^N,$

    $ -\Delta v+V(x)v=f(x,u)$ in $R^N,$

    $ u(x)\to 0$ and $v(x)\to 0$ as $|x|\to\infty,$

    where the potential $V$ is periodic and has a positive bound from below, $f(x,t)$ and $g(x,t)$ are periodic in $x$ and superlinear but subcritical in $t$ at infinity. By using generalized Nehari manifold method, existence of a positive ground state solution as well as multiple solutions for odd $f$ and $g$ are obtained.

    Mathematics Subject Classification: Primary: 35J50; Secondary: 35J55.


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