Liouville-Type Theorem for a Subelliptic Equation with Choquard Nonlinearity and Weight

In this paper, we study the subelliptic equation with weight
$$ -\Delta_\lambda u= \bigg(\frac{1}{|x|_\lambda^{Q-\alpha}}*|x|^\beta_\lambda|u|^p\bigg)|x|^\beta_\lambda|u|^{p -2}u , \qquad x\in\mathbb R^N, $$
where $\alpha>0,$ $ \beta\geq 0$, $p>2$, and $\Delta_\lambda$ is a subelliptic operator of the form
$$ \Delta_\lambda=\sum_{i=1}^N \partial_{x_i}(\lambda_i^2\partial_{x_i}). $$
Here $Q$ is the homogeneous dimension on $\mathbb R^N$ associated with the operator $\Delta_\lambda$, and the $\lambda_i$, $i=1,\dots,N$, satisfy some general hypotheses. Our purpose is to establish the nonexistence of nontrivial stable solutions for
$$ \max(Q-4-2\beta,0)<\alpha<Q. $$