Asymptotic behavior of positive solutions of inhomogeneous semilinear elliptic equations
type: Item
instance of: scholarly article
title: Asymptotic behavior of positive solutions of inhomogeneous semilinear elliptic equations
zbMATH Open document ID: 1056.35061
DOI: 10.1016/S0362-546X(01)00903-8
author: Soohyun Bae
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: Let \(n\geq 3\) and \(\Delta=\sum^n_{i=1}\partial^2/\partial x^2_i\) be the Laplace operator. Let \(p>1\) and \(f\) be a continuous function in \(\mathbb{R}^n \setminus\{0\}\). The author studies the asymptotic behavior of positive solutions of the inhomogeneous elliptic equation \[ \Delta u+u^p+f(x)=0 \tag{P} \] and also establishes an existence result demonstrating the obtained asymptotic behavior. As the first step to understand the effect of \(f\) on the asymptotic behavior of solutions, the author investigates the asymptotic behavior of the positive radial solutions of the special equation \[ \Delta u+u^p+ d|x|^{-l} =0, \] near \(\infty\) for some \(d>0\) and \(l\geq 2p/(p-1)\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1836652
zbMATH Keywords: Laplace operator
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: positive solutions
zbMATH Keywords: inhomogeneous elliptic equation
zbMATH Keywords: existence
zbMATH Keywords: positive radial solutions
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1836652