Uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains

• DOI: 10.1016/j.jmaa.2018.11.037
• Publication Date: 2018-11-14T16:49:39Z
• Authors: K.D. Chu; D.D. Hai; R. Shivaji
• Keywords: 0211 other engineering and technologies; 02 engineering and technology

Abstract We prove uniqueness and asymptotic behavior of positive radial solutions to the p-Laplacian problem { − Δ p u = λ K ( | x | ) f ( u ) in | x | > r 0 , u = 0 on | x | = r 0 , u ( x ) → 0 as | x | → ∞ , where Ω = { x ∈ R n : | x | > r 0 > 0 } , n > p , f : ( 0 , ∞ ) → R is continuous, f ( u ) ∼ u q at ∞ for some q ∈ [ 0 , p − 1 ) with possible infinite semipositone structure at 0, and λ is a large parameter.