Abstract
We investigate here the following weighted degenerate elliptic system
-Delta(s)u = (1 + parallel to x parallel to(2(s+1)))(alpha/2(s+1))v(p), -Delta(s)v = (1 + parallel to x parallel to(2(s+1)))(alpha/2(s+1))u(theta),
u, v > 0 in R-N := R-N1 x R-N2,
where Delta(s) = Delta(x) + vertical bar x vertical bar(2s)Delta(y), is the Grushin operator, s, alpha >= 0 and 1 < p <= theta. Here
parallel to x parallel to = (vertical bar x vertical bar(2(s+1)) + vertical bar y vertical bar(2))(1/2(s+1)) and x := (x, y) is an element of R-N := R-N1 x R-N2.
In particular, we establish some new Liouville-type theorems for stable solutions of the system, which recover and considerably improve upon the known results (Duong and Phan in J. Math. Anal. Appl. 454(2):785-801, 2017; Hajlaoui et al. in Discrete Contin. Dyn. Syst. 37:265-279, 2017).