Abstract
We examine the general weighted Lane-Emden system
-Delta u = rho(x)v(p), -Delta v = rho(x)u(theta), u,v > 0 in R-N
where 1 < p <= theta and rho : R-N -> R is a radial continuous function satisfying rho(x) >= A(1 + vertical bar x vertical bar(2))(alpha/2) in R-N for some alpha >= 0 and A > 0. We prove some Liouville type results for stable solution and improve the previous works [2, 9, 12]. In particular, we establish a new comparison property (see Proposition 1 below) which is crucial to handle the case 1 < p <= 4/3. Our results can be applied also to the weighted Lane-Emden equation -Delta u = rho(x)u(p) in R-N.