Liouville type theorems for stable solutions of the weighted elliptic system

We examine the weighted elliptic system{−Δu=(1+|x|2)α2v,−Δv=(1+|x|2)α2up,inRN, and prove Liouville type theorems for the classical positive and nonnegative stable solutions in higher dimension. In particular, there are no positive stable solutions for any N≤12+5αN≤12+5α, p>1p>1 and α>0α>0. Our proof is based on a combination of the bootstrap argument, Souplet's inequality and intermediate stability criterion, which is used to obtain sharp results.