Non-Existence Results for Stable Solutions to Weighted Elliptic Systems including Advection Terms

Abstract

In this paper, we study a non-linear weighted Grushin system including advection terms. We prove some Liouville-type theorems for stable solutions of the system, based on the comparison property and the bootstrap iteration. Our results generalise and improve upon some previous works.

Keywords

• Liouville-type theorem
• stable solutions
• weighted Grushin system