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,r...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11971436 and 12011530199)Natural Science Foundation of Zhejiang(Grant No.LD19A010001)。
文摘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.
