对数椭圆方程正解的存在性与唯一性  

Existence and Uniqueness of Positive Solutions for Logarithmic Elliptic Equations

作　　者：王臣熙 索洪敏 雷春雨 张鹏 WANG Chen-xi;SUO Hong-min;LEI Chun-yu;ZHANG Peng(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;School of Mathematics,Zunyi Normal University,Zunyi 563006,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025 [2]遵义师范学院数学学院,贵州遵义563006

出　　处：《遵义师范学院学报》2025年第2期91-93,115,共4页Journal of Zunyi Normal University

基　　金：国家自然科学基金(No.11661021;No.12061021)。

摘　　要：利用球面约束极小化方法,研究了下面的对数椭圆型方程{-△u=ulog|u|,x∈Ωu=0,x∈δΩ,Ω■R^(N)(N≥3)是一个具有光滑边界的有界区域.利用球面上的极小化方法,得到了正解的存在性与唯一性.Using the spherical constraint minimization method,the following logarithmic elliptic equations were studied{-△u=ulog|u|,x∈Ωu=0,x∈δΩ,whereΩ■R^(N)(N≥3)is a bounded region with smooth boundaries.The existence and uniqueness of positive solutions were obtained using the minimization method on the sphere.

关 键 词：半线性椭圆方程 对数非线性 正解 唯一性 

分 类 号：O177.91[理学—数学]