Liouville type theorems for Kirchhoff sub-elliptic equations involving Δ_λ-operators - Nguyen, Thi Thu Huong; Quyet, Dao Trong; Vu, Thi Hien Anh (Topological Methods in Nonlinear Analysis, 2023)
In this paper, we study the Kirchhoff elliptic equations of the form -M(\| abla_λ u\|^2)Δ_λ u=w(x)f(u) in R^N, where M is a smooth monotone function, w is a weight function and f(u) is of the form u^p, e^u or -u^-p. The operator Δ_λ is strongly degenerate and given by Δ_λ=_j=1^N x_j(λ_j^2(x)x_j). We shall prove some classifications of stable solutions to the equation above under general assumptions on M and λ_j, j=1,…,N.