Liouville results for stable solutions of weighted elliptic equations involving the Grushin operator

We examine the following weighted degenerate elliptic equation involving the Grushin operator: Delta(s)u+theta(s)(x ')|u|(theta-1)u=0 in R-N,N>2,theta>1, where x '=(x(1),...,x(m))is an element of R-m, 1 <= m <= N, theta(s)is an element of C(R-m,R) is a continuous positive function satisfying lim(|x '|s ->infinity) theta(s)(x ')/|x '|(alpha)(s) >0, for some alpha>-2, and Delta(s) is an operator of the form Delta(s):=Sigma(k)(i=1) partial derivative(xi)(s(i)(2)partial derivative(xi)). Under some general hypotheses of the functions si,i=1,...,k, we establish some new Liouville type theorems for stable solutions of this equation for a large classe of weights. Our results recover and considerably improve the previous works (Mtiri in Acta Appl Math 174:7, 2021; Farina and Hasegawa in Proc Royal Soc Edinburgh 150:1567, 2020).