Liouville type theorem for nonlinear elliptic equation involving Grushin operators

Abstract

In this paper, we study the nonexistence of positive solutions for the following elliptic equation [Formula: see text] where L α u = Δ x u + (α + 1) 2 |x| 2α Δ y u, α > 0, (x, y) ∈ ℝ m × ℝ k . We will prove that this problem possesses no positive solutions under some assumptions on the nonlinear term f. The main technique we use is the moving plane method in an integral form.