一类非线性薛定谔泊松方程的正解  

Positive Solutions for a Class of Nonlinear Schr dinger-Poisson Equations

作　　者：黎辰璠 陈建清 LI Chenfan;CHEN Jianqing(College of Mathematics and Informatics,Fujian Normal University,Fuzhou Fujian 350117,China)

机构地区：[1]福建师范大学数学与信息学院,福建福州350117

出　　处：《莆田学院学报》2021年第5期27-30,共4页Journal of putian University

基　　金：国家自然科学基金资助项目(11871152)。

摘　　要：用变分法和一些分析技巧讨论一类带有次临界指数且具有奇异项的非线性薛定谔泊松方程:-Δu-μu/|x|^(2)+φ_(u)(x)u=|u|^(2^(*)-2)u+θh(x)。证明了,存在θ_(*)>0,对任意θ∈(0,θ_(*)),薛定谔泊松方程存在至少一个局部极小正解。A class of nonlinear Schr dinger-Poisson problems with subcritical exponents and singular terms:-Δu-μu/|x|^(2)+φ_(u)(x)u=|u|^(2^(*)-2)u+θh(x),is discussed by using the variational method and some analytical techniques.We demonstrate that,there existsθ_(*)>0 and that for any θ∈(0,θ_(*)),the Schrodinger-Poisson equation has at least one positive solution to its local minimum.

关 键 词：薛定谔泊松方程 奇异项 SOBOLEV临界指数 变分法 

分 类 号：O175.25[理学—数学]