Critical elliptic equations via a dynamical systems approach. (May 2019)

• Record Type: Journal Article
• Authors: Ai, Shangbing; Cowan, Craig
• Is Part Of: Nonlinear analysis. Volume 182(2019)
• Page Start: 97
• Page End: 112
• Publication Date: 2019-05
• Subjects: 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.2018.12.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work we consider the existence of positive solutions to various equations of the form − Δ u ( x ) = ( 1 + g ( | x |, u ) ) u ( x ) p in B R, u = 0 on ∂ B R, where B R is the open ball of radius R in R N centered at the origin and p = N + 2 N − 2 . We will generally assume g is nonnegative. Our approach will be to utilize some dynamical systems approaches.