Uniqueness of positive solutions for a class of semipositone elliptic systems
type: Item
instance of: scholarly article
title: Uniqueness of positive solutions for a class of semipositone elliptic systems
zbMATH Open document ID: 1220.35038
author: R. Shivaji
author: D. D. Hai
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-01-11T00:00:00Z
review text: Consider the boundary value problem \[ \begin{gathered} -\Delta u=\lambda f(v),\quad -\Delta v= \mu g(u)\quad\text{for }x\in \Omega,\\ u= 0= v\quad\text{for }x\in \partial\Omega,\end{gathered}\tag{\(*\)} \] where \(\Omega\) is the open unit ball in \(\mathbb{R}^N\), \(N\geq 1\) with smooth boundary \(\partial\Omega\), \(\lambda\) and \(\mu\) are positive parameters. The authors derive conditions on \(f\) and \(g\) such \((*)\) has for sufficiently large \(\lambda\) and \(\mu\) a unique positive solution. The proof is based on a boundary value problem for an ODE-system.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5115303
MaRDI profile type: Publication
full work available at URL: j.na.2005.11.034
OpenAlex ID: W2077185809
cites work: Uniqueness and Stability of Nonnegative Solutions for Semipositone Problems in a Ball
cites work: Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearity
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: Inequalities for second-order elliptic equations with applications to unbounded domains. I
cites work: Positivity of nonnegative solutions for cooperative semipositone systems.
cites work: Symmetry properties in systems of semilinear elliptic equations
cites work: An existence result on positive solutions for a class of semilinear elliptic systems
cites work: Uniqueness of positive solutions for a class of semilinear elliptic systems
cites work: Uniqueness of positive solutions for semilinear elliptic systems
DOI: 10.1016/J.NA.2005.11.034
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description: scientific article; zbMATH DE number 5115303