In this paper, we prove the Liouville type theorem for stable W loc 1 , p solutions of the weighted quasilinear problem − div (w 1 (x) (s 2 | ∇ u | 2) p − 2 2 ∇ u) = w 2 (x) f (u) in R N , where s ≥ 0 is a real number, f (u) is either e u or − e 1 u and w 1 (x) , w 2 (x) ∈ L loc 1 (R N) be nonnegative functions so that w 1 (x) ≤ C 1 | x | m and w 2 (x) ≥ C 2 | x | n when | x | is big enough. Here we need n > m .
