Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\)
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.
nonexistence of classical positive stable solutions
scientific article; zbMATH DE number 6850164
scientific article