Sign-changing bubble tower solutions for a critical fractional problem. (October 2022)

• Record Type: Journal Article
• Authors: Chen, Wenjing; Long, Wei; Yang, Jianfu
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: 35J20 -- 35J60; Critical fractional elliptic problem -- Sign-changing bubble tower solutions -- Lyapunov Schmidt procedure; 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.2022.113054
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the following fractional elliptic problem (0.1) ( − Δ ) s u = | u | 2 s ∗ − 2 u, in Ω ɛ, u = 0, in R N ∖ Ω ɛ, where 2 s ∗ = 2 N N − 2 s is the critical exponent, 0 < s < 1, Ω ɛ = Ω ∖ B ( 0, ɛ ) with Ω being a bounded smooth domain in R N containing the origin, N > 2 s and B ( 0, ɛ ) is the ball centered at the origin with radius ɛ > 0 . We construct a sign-changing solution of (0.1) with the shape of a tower of bubbles as ɛ goes to zero.