Multiple boundary bubbling phenomenon of solutions to a Neumann problem
type: Item
instance of: scholarly article
title: Multiple boundary bubbling phenomenon of solutions to a Neumann problem
zbMATH Open document ID: 1178.35181
author: Yang Wang
author: Long Wei
published in: Advances in Differential Equations
publication date: 2009-06-30T00:00:00Z
review text: The authors are concerned with existence and asymptotic behavior of nontrivial solutions to the boundary value problem \(-\mathrm{div}(a(x)\nabla u)+a(x)u=0\) in \(\Omega\), \(\partial u/\partial \nu=\varepsilon e^{u}\) on \(\partial\Omega\). Here \(\Omega\) is a smooth bounded domain in the plane and \(\varepsilon>0\) is small. The main novelty of the paper is the presence of the smooth weight \(a(x)\) which satisfies \(0<a_1\leq a(x)\leq a_2<\infty\) in \(\Omega\). First, the authors establish a decomposition result for the regular part of the associated Green function to the above problem. This decomposition result is then used to construct nontrivial solutions with a cluster of multiple bubbles near a local maximum point of \(a(x)\) on the boundary.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35J08
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 5573010
zbMATH Keywords: elliptic problem
zbMATH Keywords: Neumann boundary condition
zbMATH Keywords: Green function
zbMATH Keywords: bubbling phenomenon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5573010