Non-existence and behaviour at infinity of solutions of some elliptic equations
type: Item
instance of: scholarly article
title: Non-existence and behaviour at infinity of solutions of some elliptic equations
zbMATH Open document ID: 1058.35014
author: Shu-Yu Hsu
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-06-18T00:00:00Z
review text: The author studies the solutions of the equation \[ \Delta v+\alpha e^v+ \beta(x\cdot\nabla v)e^v= 0\quad\text{in }\mathbb{R}^2,\tag{1} \] where \(\alpha\), \(\beta\) are constants. He shows that when \(\alpha\leq2\beta\) there does not exist any solution of (1) satisfying \(\int_{\mathbb{R}^2} e^v \,dx< \infty\) and \(| x|^2 e^{v(x)}\leq C_1\) \(\forall x\in\mathbb{R}^2\) for some constant \(C_1> 0\). When \(\alpha> 2\beta\) the author obtains an asymptotic expansion for the solution of (1) satisfying the above conditions.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2075943
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: nonexistence
zbMATH Keywords: behaviour at infinity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.2004.10.769
OpenAlex ID: W2055624372
DOI: 10.3934/DCDS.2004.10.769
description: scientific article; zbMATH DE number 2075943