Bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity. (September 2018)

• Record Type: Journal Article
• Authors: Yang, Haitao; Zhang, Yibin
• Is Part Of: Nonlinear analysis. Volume 174(2018)
• Page Start: 141
• Page End: 168
• Publication Date: 2018-09
• Subjects: Bubbling solutions -- Anisotropic elliptic problem -- Exponential nonlinearity -- Lazer–McKenna conjecture -- 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.2018.04.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let Ω be a bounded domain in R 2 with smooth boundary, we study the following anisotropic elliptic problem − ∇ ( a ( x ) ∇ υ ) = a ( x ) [ e υ − s ϕ 1 − h ( x ) ] in Ω, υ = 0 on ∂ Ω, where a ( x ) is a positive smooth function, h ∈ C 0, α ( Ω ¯ ), s > 0 is a large parameter and ϕ 1 is a positive first eigenfunction of the problem − ∇ ( a ( x ) ∇ ϕ ) = λ a ( x ) ϕ under Dirichlet boundary condition in Ω . We construct solutions of this problem which exhibit multiple concentration behavior around maximum points of a ( x ) ϕ 1 in the domain as s → + ∞ .