分数阶Schrodinger-Poisson系统规范化解的存在性  

Existence of Normalized Solutions for Fractional Schrodinger-Poisson System

作　　者：孙霞 滕凯民 SUN Xia;TENG Kaimin(College of Mathematics,Taiyuan University of Technology,Jinzhong 030600,China)

机构地区：[1]太原理工大学数学学院,山西晋中030600

出　　处：《应用数学》2020年第3期666-680,共15页Mathematica Applicata

基　　金：国家自然科学基金(11501403);山西省留学回国择优项目(2018)。

摘　　要：本文研究分数阶Schrodinger-Poisson系统规范化解的存在性,首先在变分框架下将其规范化解转化为约束极小化问题的极小元,然后利用集中紧性原理证明了极小元的存在性与不存在性.This paper is devoted to studying the existence of the normalized solutions for fractional Schrodinger-Poisson system.We first transform the normalized solutions into minimizers of the constraint minimization problem under the variational framework,then the existence and nonexistence of the minimizers are proved by the concentration-compactness principle.

关 键 词：分数阶Schrodinger-Poisson系统 变分法 集中紧性原理 规范化解 

分 类 号：O175.25[理学—数学]