Multiple solutions for a Schrdinger-Poisson-Slater equation with external Coulomb potential

作     者：JIANG YongSheng ZHOU HuanSong 

作者机构：School of Statistics and MathematicsZhongnan University of Economics and Law Wuhan Institute of Physics and MathematicsChinese Academy of Sciences 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第6期

页      面：1163-1174页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11071245,11171339 and 11201486) supported by the Fundamental Research Funds for the Central Universities 

主　　题：泊松方程 库仑势 莱特 非平凡解 薛定谔 物理学 实数 基态 

摘      要：Consider the following Schrdinger-Poisson-Slater system,(P)u+ω-β|x|u+λφ(x)u=|u|p-1u,x∈R3,-φ=u2,u∈H1(R3),whereω0,λ0 andβ0 are real numbers,p∈(1,2).Forβ=0,it is known that problem(P)has no nontrivial solution ifλ0 suitably ***β0,-β/|x|is an important potential in physics,which is called external Coulomb *** this paper,we find that(P)withβ0 has totally different properties from that ofβ=***β0,we prove that(P)has a ground state and multiple solutions ifλcp,ω,where cp,ω0 is a constant which can be expressed explicitly viaωand p.