Qualitative properties and classification of solutions to elliptic equations with Stein-Weiss type convolution part  

作　　者：Xiang Li Minbo Yang Xianmei Zhou 

机构地区：[1]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Science China Mathematics》2022年第10期2123-2150,共28页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11971436 and 12011530199);Natural Science Foundation of Zhejiang(Grant No.LD19A010001)。

摘　　要：In this paper,we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part.Firstly,we study the qualitative properties,such as the symmetry,regularity and asymptotic behavior of the positive solutions.Secondly,we classify the non-positive solutions by proving some Liouville type theorems for the finite Morse index solutions and stable solutions to the nonlocal elliptic equations with double weights.

关 键 词：weighted elliptic equation finite Morse index solution Liouville type theorems qualitative properties 

分 类 号：O175.25[理学—数学]