Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\) (Q1705180)

This paper concerns the nonexistence of classical positive stable solutions for the weighted elliptic system \[ -\omega(x)\Delta u-\nabla w(x)\cdot \nabla u=\omega_1 v^{\vartheta}, \] \[ -\omega(x)\Delta v-\nabla w(x)\cdot \nabla v=\omega_2 v^p, \] posed in \(\mathbb{R}^N\), \(N\geq 3\), \(p\geq \vartheta >1\) and \(\omega, \omega_1,\omega_2\) satisfy some appropriate conditions. The two main results of the paper establish that under some extra conditions on exponents and weights, the above system has no classical positive stable solutions.