On Stable Weak Solutions to Double‐Phase Problems Involving the Grushin Operator

ABSTRACT In this paper, we prove Liouville‐type theorems for the double‐phase problem where satisfy some appropriate conditions at infinity. (resp., ) is Grushin divergence (resp., Grushin gradient). We establish various Liouville‐type theorems for nontrivial weak solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether unbounded or sign‐changing) under certain assumptions. The main methods we use are energy estimation and a Pohožaev type identity.