Nonlinear fractional elliptic problem with singular term at the boundary. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Abdellaoui, B.; Biroud, K.; Primo, A.
• Is Part Of: Complex variables and elliptic equations. Volume 64:Issue 6(2019)
• Page Start: 909
• Page End: 932
• Publication Date: 2019-06-03
• Subjects: V. Radulescu; Fractional Laplacian -- Hardy inequality -- critical problem -- singular weight -- blow-up arguments; 35D05 -- 35D10 -- 35J20 -- 35J25 -- 35J70; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2018.1487410
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: LetΩ ⊂ R N be a bounded regular domain, 0< s <1 and N >2 s . We consider ( − D ) s u = u q d 2 s in Ω, u > 0 in Ω, u = 0 in R N ∖ Ω, where0 < q ≤ 2 ∗ − 1, 0< s <1 andd ( x ) = dist ( x, ∂Ω ) . The main goal of this paper is to analyse existence and non-existence of solution to problem (P) according to the values of s and q .