Quang Thanh Khuat, “Liouville-type theorems for double phase problems involving the Grushin operator”, In this paper, we are concerned with the double phase problem involving the Grushin operator in the whole space $\mathbb R^{N}=\mathbb R^{N_1}\times\mathbb R^{N_2}$
\begin{equation*}
- \text {div}_G (|\nabla_G u|^{p-2}\nabla_G u + w(z) |\nabla_G u|^{q-2}\nabla_G u)= f(z)|u|^{r-1}u ,
\end{equation*}
where $\nabla_G$ is the Grushin gradient, $\Delta_G$ is the Grushin operator, $q\geq p \geq 2, r>q-1 $ and $w, f \in L^1_{\loc}(\mathbb{R}^N)$ are two nonnegative functions satisfying some growth conditions at infinity. Our purpose is to establish some Liouville-type theorems for stable weak solutions or for weak solutions which are stable outside a compact set of the equation above., Zeitschrift für Analysis und ihre Anwendungen, 43:N0.1/2 (2024), 237-257
