LOCALIZED NODAL SOLUTIONS FOR SCHRODINGER-POISSON SYSTEMS  

作　　者：Xing WANG Rui HE Xiangqing LIU 王星;何锐;刘祥清(Department of Mathematics,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]Department of Mathematics,Yunnan Normal University,Kunming 650500,China

出　　处：《Acta Mathematica Scientia》2022年第5期1947-1970,共24页数学物理学报（B辑英文版）

基　　金：Supported by NSFC(12161093).

摘　　要：In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.

关 键 词：Schrodinger-Poisson systems localized nodal solutions perturbation method 

分 类 号：O175[理学—数学]