Existence and non-existence of positive solutions of nonlinear elliptic systems and the biharmonic equation
type: Item
instance of: scholarly article
title: Existence and non-existence of positive solutions of nonlinear elliptic systems and the biharmonic equation
zbMATH Open document ID: 0758.35029
published in: Differential and Integral Equations
publication date: 1993-01-16T00:00:00Z
review text: The object of the paper is to give some a priori estimates allowing to prove existence and non-existence theorems for particular elliptic systems and the biharmonic equation. The authors consider systems of the form \[ -\Delta u=g(v),\;v>0 \text{ in } B_ R,\quad -\Delta v=f(u),\;u>0\text{ in } B_ R,\quad u=0,\;v=0\text{ on }\partial B_ R, \] where \((u,v)\in C^ 2(\overline B_ R)\times C^ 2(\overline B_ R)\), with \(B_ R\) a ball in \(\mathbb{R}^ N\) \((N\geq 4)\) of radius \(R\), while \(f,g\in C(\mathbb{R})\) with \(f(0)=g(0)=0\).
reviewed by: Antonio Bove
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 31A30
zbMATH DE Number: 90502
zbMATH Keywords: radially symmetric solutions
author: Lambertus A. Peletier
author: Robert Vandervorst
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 90502