On a weighted Lane–Emden system. Issue 5 (3rd April 2020) - Guan, Xiaohong; Mei, Linfeng
ABSTRACT: Liouville type results for positive radial entire solutions ( u, v ) ∈ [ C 2 ( R N ∖ { 0 } ) ∩ C 0 ( R N ) ] × [ C 2 ( R N ∖ { 0 } ) ∩ C 0 ( R N ) ] ( N ≥ 3 ) of the weighted Lane–Emden system div ( | x | θ 1 ∇ u ) + | x | l 1 v p = 0 in   R N ∖ { 0 }, div ( | x | θ 2 ∇ v ) + | x | l 2 u q = 0 in   R N ∖ { 0 } are established, where ( p, q ) ∈ ( 0, ∞ ) × ( 0, ∞ ), θ 1, θ 2, l 1, l 2 satisfy N + θ i > 2, τ i = l i − θ i > − 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 radial solutions of the Dirichlet problem of this system in the unit ball are also obtained.