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arXiv · 1802.02539

Multiple positive bound states for critical Schr\"odinger-Poisson systems

Giovanna Cerami·Riccardo Molle
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Abstract

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schr\"odinger-Poisson system: $$ \left\{ \begin{array}{l} \vspace{2mm} -\Delta u+V(x)u+K(x)\phi(x)u=u^5 -\Delta \phi =K(x)u^2\qquad x\in\R^3 \end{array}\right.\quad\quad (SP) $$ We remark that $(SP)$ exhibits a "double" lack of compactness because of the unboundedness of $\R^3$ and the critical growth of the nonlinear term and that in our assumptions ground state solutions of $(SP)$ do not exist.

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Giovanna Cerami, Riccardo Molle. 2018-02-07. Multiple positive bound states for critical Schr\"odinger-Poisson systems. https://arxiv.org/abs/1802.02539

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