摘要
该文主要研究下面的Schrodinger-Maxwell方程{△Ф=(K(x)+α)u^2,(x,u)∈(R^3,R)-△u+V(x)u-(K(x)+α)Фu=β|u|^4u+b(x)|u|^p-1u,(x,u)∈(R^3,R)基态解的存在性,其中β是正常数.当V和K以及b(x)满足某些假设条件时,运用变分法和临界点理论,可以证明当α< 0和p∈(3,4)时,上面的方程至少存在一个基态解.
In this paper, we study the existence of the ground state solutions for the following Schrodinger-Maxwell equations {△Ф=(K(x)+α)u^2,(x,u)∈(R^3,R)-△u+V(x)u-(K(x)+α)Фu=β|u|^4u+b(x)|u|^p-1u,(x,u)∈(R^3,R) where β is a positive constant. Under some assumptions on V, K and b(x), by using the variational method and critical point theorem, we prove that such a class of equations has at least a ground state solution for α< 0 and p ∈(3, 4).
作者
方立婉
黄文念
汪敏庆
Liwan Fang;Wennian Huang;Minqing Wang(School of Mathematics and Computer Science, Guangxi Science and Technology Normal University,Guangxi Laibin 546199;School of Mathematics and Statistics, Guangxi Normal University, Guangxi Guilin 541004)
出处
《数学物理学报（A辑）》
CSCD
北大核心
2019年第3期475-483,共9页
Acta Mathematica Scientia
基金
广西师范大学科学研究基金(2014ZD001)
广西自然科学基金(2015GXNSFBA139018)
2017广西研究生教育创新计划项目(XYCZ2017074)~~
