Positive rotationally symmetric solutions for a Dirichlet problem involving the higher mean curvature operator in Minkowski space
type: Item
instance of: scholarly article
title: Positive rotationally symmetric solutions for a Dirichlet problem involving the higher mean curvature operator in Minkowski space
zbMATH Open document ID: 1384.53018
author: Man Xu
author: Ruyun Ma
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-01-11T00:00:00Z
review text: The paper deals with the global behavior of positive rotationally symmetric solutions to a Dirichlet problem involving the \(k\)-th mean curvature operator in the Minkowski space \(\mathbb{L}^{n+1}.\) Precisely, the authors study the structure of positive (or negative) solutions to the problem \[ \big(r^{n-k}\phi^k(v')\big)'=\lambda n r^{n-1} H_k(v(r),r), \quad r\in (0,R), \] \[ |v'|<1,\quad r\in(0,R), \] \[ v'(0)=0=v(R), \] where \(\lambda\) is a positive parameter, \(\phi(s)=s/\sqrt{1-s^2}\) and \(H_k\) is a given continuous function. The proofs make use of global bifurcation techniques.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 6824850
zbMATH Keywords: higher mean curvature function
zbMATH Keywords: Minkowski spacetime
zbMATH Keywords: positive solution
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.11.049
OpenAlex ID: W2773443799
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DOI: 10.1016/J.JMAA.2017.11.049
description: scientific article; zbMATH DE number 6824850