R^(3)中一类Schrodinger-Poisson系统约束极小元的存在性

Existence of Normalized Minimizers for a Class of Schrodinger-Poisson System in R^(3)

【目的】研究R^(3)中一类带有一般项的Schrodinger-Poisson系统在指定L^(2)范数下基态解的存在性。【方法】运用集中紧性原理、Brézis-Lieb引理及一些分析方法进行了研究。【结果】首先得到了系统的能量泛函在约束下的下确界是可达的,然后找到了能量泛函的约束极小元。【结论】当非线性项满足适当假设条件时,基态解存在。

[Purposes]The existence of ground state solutions for a class of Schrodinger-Poisson system with a general term in R^(3)under a given L^(2)norm is studied.[Methods]The Lions’concentration-compactness principle,Brézis-Lieblemma and some analytical methods are used to study this system.[Findings]Firstly,the infimum of the energy functional of the system is reachable under constraints.Secondly the normalized minimizers of the energy functional is found.[Conclusions]The ground state solution exists when the nonlinear term satisfies certain assumptions.