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arXiv · 1408.6383

Quantitative Properties on the Steady States to A Schrödinger-Poisson-Slater System

Changlin Xiang
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Abstract

A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -ΔQ+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -ΔV=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 & \mbox{as }x\to\infty. \end{cases} \] is given in this paper: existence, uniqueness, regularity and asymptotic behavior at infinity, where $C_{S}>0$ is a constant. To the author's knowledge, this is the first uniqueness result on SPS system.

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Changlin Xiang. 2014-08-27. Quantitative Properties on the Steady States to A Schrödinger-Poisson-Slater System. https://arxiv.org/abs/1408.6383

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