A uniqueness theorem for some nonlinear boundary value problem with a large parameter
type: Item
instance of: scholarly article
title: A uniqueness theorem for some nonlinear boundary value problem with a large parameter
zbMATH Open document ID: 0544.35046
DOI: 10.1007/BF01473435
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182967
review text: Let \(-Au=a_{ij}u_{ij}+a_ iu_ i-a_ 0u\) denote a uniformly elliptic operator with Hölder-continuous coefficients and \(a_ 0\geq 0\). A short and simple proof is given, that the nonlinear boundary value problem \(Au=\lambda f(x,u)\) in \(\Omega\), \(u|_{\partial \Omega}=0\) has a unique positive solution for all \(\lambda\) sufficiently large, if f is positive and (roughly) \(f\sim u^{-\gamma}\), \(| \partial f/\partial u| \sim u^{-\gamma -1}\) for \(u\to \infty\) with some \(\gamma \in [0,1)\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3865820
zbMATH Keywords: uniqueness
zbMATH Keywords: Hölder-continuous coefficients
zbMATH Keywords: positive solution
author: Michael Wiegner
MaRDI profile type: Publication
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: Elliptic Partial Differential Equations of Second Order
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
cites work: About uniqueness for nonlinear boundary value problems
OpenAlex ID: W1980174403
description: scientific article; zbMATH DE number 3865820