On a weighted Lane–Emden system. Issue 5 (3rd April 2020)

• Record Type: Journal Article
• Authors: Guan, Xiaohong; Mei, Linfeng
• Is Part Of: Applicable analysis. Volume 99:Issue 5(2020)
• Page Start: 814
• Page End: 839
• Publication Date: 2020-04-03
• Subjects: Daomin Cao; Singular positive radial solutions -- existence and non-existence -- weighted Lane–Emden system; Primary 35B45 -- Secondary 35J40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1514017
• Languages: English
• ISSNs: 0003-6811

Abstract

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.