Liouville type theorems for elliptic equations involving Grushin operator and advection
| dc.contributor.author | Duong, Anh Tuan | |
| dc.contributor.author | Nguyen, Nhu Thang | |
| dc.date.accessioned | 2022-04-12T13:08:15Z | |
| dc.date.available | 2022-04-12T13:08:15Z | |
| dc.date.issued | 2017-04-25 | |
| dc.description.abstract | In 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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 11 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Duong, 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15640 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Liouville type theorem | |
| dc.subject | Stable weak solution | |
| dc.subject | Grushin operator | |
| dc.subject | Degenerate elliptic equation | |
| dc.title | Liouville type theorems for elliptic equations involving Grushin operator and advection | en_US |
| dc.type | Article |