Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities. (January 2022)

• Record Type: Journal Article
• Authors: Wu, Ke
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: Rigidity results -- Asymptotic behavior -- Removable singularity; 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.2021.112594
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the asymptotic behavior of positive solutions of the biharmonic equation Δ 2 u = u p in B 2 ∖ { 0 } with an isolated singularity, where the punctured ball B 2 ∖ { 0 } ⊂ R n with n > 5 and p > ( n + 4 ) / ( n − 4 ) . We classify isolated singularities of positive solutions and describe the asymptotic behavior of positive singular solutions without the sign assumption for − Δ u .