About uniqueness for nonlinear boundary value problems
type: Item
instance of: scholarly article
title: About uniqueness for nonlinear boundary value problems
zbMATH Open document ID: 0537.35038
DOI: 10.1007/BF01455970
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163913
review text: Let A be a general second order elliptic operator in the bounded domain \(\Omega\) and let f:\({\bar \Omega}\times R^+\to R^+\) be Hölder continuous in \(x\in \Omega\) and continuously differentiable in \(\zeta \in R^+\). The author considers the semilinear equation (1) \(Au=\lambda f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial \Omega\) under some positivity and growth assumptions for f and proves the following: Theorem. There exists a \(\lambda_ 0>0\) such that (1) has a unique solution for \(\lambda>\lambda_ 0\).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 3853610
zbMATH Keywords: uniqueness
zbMATH Keywords: semilinear equation
author: Vladimir Schuchman
MaRDI profile type: Publication
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: Q5548618
cites work: Symmetry and related properties via the maximum principle
cites work: On the Existence of Positive Solutions of Semilinear Elliptic Equations
OpenAlex ID: W2025499518
description: scientific article; zbMATH DE number 3853610