Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity
type: Item
instance of: scholarly article
title: Sign-changing blow-up solutions for Hénon type elliptic equations with exponential nonlinearity
zbMATH Open document ID: 1323.35034
author: Teresa D'Aprile
published in: Journal of Functional Analysis
publication date: 2015-08-26T00:00:00Z
review text: The paper deals with the existence of sign-changing solutions with multiple concentration to the Dirichlet problem \[ \begin{cases} -\Delta u=\varepsilon^2| x|^{2\alpha} (e^u-e^{-u}) & \text{in }\Omega,\\ u=0 & \text{on }\partial\Omega, \end{cases} \] where \(\alpha>0\), \(\Omega\) is a smooth and bounded domain in \(\mathbb R^2\) which contains the origin, and \(\varepsilon>0\) is a small parameter. It is proved that if \(\alpha\neq 1\) then a nodal solution exists with a number of mixed positive and negative blow-up points up to 4.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 6475676
zbMATH Keywords: Hénon type equation
zbMATH Keywords: blow-up solutions
zbMATH Keywords: finite-dimensional reduction
zbMATH Keywords: min-max argument
MaRDI profile type: Publication
full work available at URL: j.jfa.2015.02.009
OpenAlex ID: W1977436583
DOI: 10.1016/J.JFA.2015.02.009
description: scientific article; zbMATH DE number 6475676