On the conformal Gaussian curvature equation in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: On the conformal Gaussian curvature equation in \(\mathbb{R}^2\)
zbMATH Open document ID: 0911.35044
author: Kuo-Shung Cheng
author: Chang-Shou Lin
published in: Journal of Differential Equations
publication date: 1999-05-04T00:00:00Z
review text: The authors study the equation \[ \Delta u+K(x)e^{2u}=0\quad\text{on }\mathbb{R}^2 \] where \(K=K(| x|)\) and \(K\) does not decay for large values of \(| x|\). The best possible range for the total curvature is investigated in the context of radial solutions. Moreover, it is shown by examples that when \(K(x)\) is negative for \(| x|\) large, the equation has a branch of solutions which satisfies some monotonicity property.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1206642
zbMATH Keywords: prescribing Gaussian curvature
zbMATH Keywords: total curvature
zbMATH Keywords: branch of solutions
zbMATH Keywords: monotonicity property
reviewed by: M. Fuchs
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3424
OpenAlex ID: W1998104535
cites work: An Extension of Schwarz's Lemma
cites work: On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
cites work: On the asymptotic behavior of solutions of the conformal Gaussian curvature equations in \(\mathbb R^ 2\)
cites work: On the structure of the conformal Gaussian curvature equation on \({\mathbb{R}}^ 2\)
cites work: On the structure of the conformal Gaussian curvature equation on \(R^ 2\). II
cites work: Conformal Metrics with Prescribed Gaussian Curvature on S 2
cites work: Q3336320
cites work: ON THE EQUATION Δu+k(x)eu= 0
cites work: Q5646042
DOI: 10.1006/JDEQ.1998.3424
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description: scientific article; zbMATH DE number 1206642