PROPERTIES OF SOLUTIONS TO A HARMONIC-MAPPING TYPE EQUATION WITH A DIRICHLET BOUNDARY CONDITION  

作　　者：陈博 陈正茂 谢君辉 Bo CHEN;Zhengmao CHEN;Junhui XIE(School of Mathematics and Statistics,Hubei Minzu University,Enshi,445000,China;School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China)

机构地区：[1]School of Mathematics and Statistics,Hubei Minzu University,Enshi,445000,China [2]School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China

出　　处：《Acta Mathematica Scientia》2023年第3期1161-1174,共14页数学物理学报（B辑英文版）

基　　金：The first author and the third author were supported by the National Natural Science Foundation of China (11761030);the Cultivation Project for High-Level Scientific Research Achievements of Hubei Minzu University (PY20002);The second author was supported by the China Postdoctoral Science Foundation (2021M690773)。

摘　　要：In the present paper, we consider the problem {-△u=u^(β_(1))|■u|^(β_(2)),in Ω,u=0,on ■Ω,u>0,in Ω,(0.1) where β_(1), β_(2) > 0 and β_(1) + β_(2) < 1, and Ω is a convex domain in R~n. The existence, uniqueness,regularity and (2-β_(2))/(1-β_(1)-β_(2))-concavity of the positive solutions of the problem(0.1) are proven.

关 键 词：Harmonic-Mappings type equation positive solution existence regularity α-concavity 

分 类 号：O175[理学—数学]