Bubble solutions for Hénon type equation with nearly critical exponent in RN. (December 2021)

• Record Type: Journal Article
• Authors: Liu, Zhongyuan
• Is Part Of: Nonlinear analysis. Volume 213(2021)
• Publication Date: 2021-12
• Subjects: 35J60 -- 35J05 -- 35J15; Bubble solution -- Hénon type equation -- Critical exponent; 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.2021.112507
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the Hénon type equation − Δ u + a ( x ) u = | x | α u p α − ε in R N, where p α = N + 2 + 2 α N − 2, α > 0, ε > 0, N ≥ 7 . We construct, for ε small enough, a family of positive solutions concentrating at the origin under certain conditions on the potential a ( x ) .