Partially symmetric solutions of the generalized Hénon equation in symmetric domains
type: Item
instance of: scholarly article
title: Partially symmetric solutions of the generalized Hénon equation in symmetric domains
zbMATH Open document ID: 1388.35068
DOI: 10.12775/TMNA.2015.043
author: Ryuji Kajikiya
published in: Topological Methods in Nonlinear Analysis
publication date: 2017-05-08T00:00:00Z
review text: The paper is concerned with the existence of partially symmetric positive solutions of the Dirichlet problem for the generalized Hénon equation: \[ -\triangle u=f(x)u^p \] on a bounded domain of the Euclidian space. The author first recalls the definition of least energy solutions in the Nehari manifold as well as the definition of \(G,H\)-invariant least energy solutions. The function \(f\) is bounded but satisfies some sign conditions. The author is interested in the existence of \(H\)-invariant solutions that could or could not be \(G\)-invariant solutions. This is the main result of the paper which is illustrated by five examples in some special situations. In the remaining part of the paper, the author develops very sharp variational inequalities that lead to the proof of the main existence result.
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 6712684
zbMATH Keywords: Hénon equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: least energy solutions
zbMATH Keywords: variational methods
reviewed by: Smail Djebali
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6712684