Blow up boundary solutions of some semilinear fractional equations in the unit ball. (July 2016)

• Record Type: Journal Article
• Authors: Ben Chrouda, Mohamed; Ben Fredj, Mahmoud
• Is Part Of: Nonlinear analysis. Volume 140(2016)
• Page Start: 236
• Page End: 253
• Publication Date: 2016-07
• Subjects: 31B05 -- 31B25 -- 35J61; Fractional Laplacian -- Semilinear equation -- Large solution -- Fractional Dirichlet problem -- Green function -- Martin kernel; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.03.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For γ > 0, we are interested in blow up solutions u ∈ C + ( B ) of the fractional problem in the unit ball B . We distinguish particularly two orders of singularity at the boundary: solutions exploding at the same rate than δ α 2 − 1 ( δ denotes the Euclidean distance) and those higher singular than δ α 2 − 1 . As a consequence, it will be shown that the classical Keller–Osserman condition cannot be readopted in the fractional setting.