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Concentration phenomena at saddle points of potential for Schrödinger-Poisson systems

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The third named author was supported by NSFC(No.11871123)
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  • We consider in $ \mathbb R^3 $ the singularly perturbed Schrödinger-Poisson system

    $ \begin{equation*} \begin{cases} - \varepsilon^2\Delta v+V(x)v+\phi(x)v = f(v)\\ - \Delta\phi = v^2 . \end{cases} \end{equation*} $

    Using variational techniques, we construct solutions which concentrate around the saddle points of the external potential $ V $, as $ \varepsilon \rightarrow 0 $.

    Mathematics Subject Classification: Primary: 35J47, Secondary: 35J50, 35J61.


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