数学
紧凑空间
多重性(数学)
泊松分布
薛定谔猫
兰姆达
截断(统计)
超临界流体
数学物理
补语(音乐)
组合数学
数学分析
物理
量子力学
热力学
统计
生物化学
化学
互补
基因
表型
出处
期刊:Topological Methods in Nonlinear Analysis
[Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University]
日期:2023-12-31
卷期号:: 1-26
被引量:1
标识
DOI:10.12775/tmna.2022.075
摘要
In this paper we are concerned with normalized solutions to the Schrödinger-Poisson system with doubly critical growth \[ \begin{cases} -\Delta u-\phi |u|^3u=\lambda u+\mu|u|^{q-2}u+|u|^4u, &x \in \R^{3},\\ -\Delta \phi=|u|^5, &x \in \R^{3}, \end{cases} \] and prescribed mass \[ \int_{\R^3}|u|^2dx=a^2,\] where $a> 0$ is a constant, $\mu> 0$ is a parameter and $2< q< 6$. In the $L^2$-subcritical case, we study the multiplicity of normalized solutions by applying the truncation technique, and the genus theory; and in the $L^2$-supercritical case, we obtain a couple of normalized solutions by developing a fiber map. Under both cases, to recover the loss of compactness of the energy functional caused by the critical growth, we need to adopt the concentration-compactness principle. Our results complement and improve some related studies for the Schrödinger-Poisson system with nonlocal critical term in the literature.
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