Blow-up of ground states of fractional Choquard equations. (December 2022)

• Record Type: Journal Article
• Authors: Vilasi, Luca; Wang, Youjun
• Is Part Of: Nonlinear analysis. Volume 225(2022)
• Publication Date: 2022-12
• Subjects: 35A15 -- 35J60 -- 35B40; Choquard equation -- Fractional Laplacian -- Blow-up; 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.2022.113117
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the blow-up behavior of ground states of the fractional Choquard equation ( − Δ ) s u + u = ( K α ∗ | u | p ϵ ) | u | p ϵ − 2 u in R N, with s ∈ ( 0, 1 ), N > 4 s, K α Riesz potential of order α ∈ ( 0, N ), as the exponent p ϵ approaches the upper critical growth regime in Hardy–Littlewood–Sobolev's inequality. We prove that the ground state u ϵ blows up in the sense that ‖ u ϵ ‖ L ∞ ( R N ) = o ϵ − N − 2 s 4 s as ϵ → 0 + .