Global continua of positive solutions for equations with nondifferentiable operators
type: Item
instance of: scholarly article
title: Global continua of positive solutions for equations with nondifferentiable operators
zbMATH Open document ID: 0938.47047
author: Nguyen Bich Huy
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-01-05T00:00:00Z
review text: Existence of global continua of solutions to nonlinear fixed point equations \(x= f(\lambda, x)\), where \(f:[0,+\infty)\times K\to K\) is a completely continuous operator in the cone \(K\), in the sense that the unbounded continuum \(S\) is such that \(S\cap\partial G\neq\emptyset\) for every bounded open set \(G\) containing the origin is studied. The author gives two variants of previous work by Amann, Bahtin and Dancer. In the first case, \(f\) has a monotone minorant and in the second a Hammerstein operator and a priori estimates are involved. An application to periodic solutions of the ordinary differential equation \(-x''= f(x, x')\) under suitable assumptions is also given.
reviewed by: Jesús Hernández
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 1384934
zbMATH Keywords: existence of global continua of solutions
zbMATH Keywords: nonlinear fixed point equations
zbMATH Keywords: monotone minorant
zbMATH Keywords: Hammerstein operator
zbMATH Keywords: a priori estimates
zbMATH Keywords: periodic solutions
zbMATH Keywords: ordinary differential equation
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6582
OpenAlex ID: W2044490861
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: Global solution branches for positive mappings
cites work: NONTRIVIAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SEMILINEAR ELLIPTIC EQUATIONS
cites work: Q5732050
cites work: Q3336252
DOI: 10.1006/JMAA.1999.6582
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description: scientific article; zbMATH DE number 1384934