Duong, Anh TuanNguyen, Nhu Thang2022-04-122022-04-122017-04-25Duong, A. T., & Nguyen, N. T. (2017). Liouville type theorems for elliptic equations involving Grushin operator and advection. <i>Electronic Journal of Differential Equations, 2017</i>(108), pp. 1-11.1072-6691https://hdl.handle.net/10877/15640In this article, we study the equation -Gαu + ∇Gw ∙ ∇Gu = ∥x∥s|u|p-1u, x = (x, y) ∈ ℝN = ℝN1 x ℝN2, where Gα (resp., ∇G) is Grushin operator (resp. Grushin gradient), p > 1 and s ≥ 0. The scalar function w satisfies a decay condition, and ∥x∥ is the norm corresponding to the Grushin distance. Based on the approach by Farina [8], we establish a Liouville type theorem for the class of stable sign-changing weak solutions. In particular, we show that the nonexistence result for stable positive classical solutions in [4] is still valid for the above equation.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalLiouville type theoremStable weak solutionGrushin operatorDegenerate elliptic equationArticle