On a weighted Lane–Emden system

Liouville type results for positive radial entire solutions (u,v)∈[C2(RN∖{0})∩C0(RN)]×[C2(RN∖{0})∩C0(RN)] (N≥3) of the weighted Lane–Emden system div(|x|θ1∇u)+|x|l1vp=0in RN∖{0},div(|x|θ2∇v)+|x|l2uq=0in RN∖{0} are established, where (p,q)∈(0,∞)×(0,∞), θ1,θ2,l1,l2 satisfy N+θi>2,τi=li−θi>−2, i=1,2. Meanwhile, classification of singularities at the origin of positive radial solutions of this system on the punctured unit ball and singular positive...