Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type
type: Item
instance of: scholarly article
title: Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type
zbMATH Open document ID: 1276.47072
author: Maher Berzig
author: Bessem Samet
publication date: 2012-11-15T00:00:00Z
review text: In this paper, the authors prove some Meir-Keeler type fixed point theorems for mixed monotone mappings in ordered Banach space. Then, the obtained results are applied to study the existence and uniqueness of positive solutions for some boundary value problems.
reviewed by: Yuqiang Feng
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6107836
zbMATH Keywords: fixed point
zbMATH Keywords: ordered Banach space
zbMATH Keywords: cone
zbMATH Keywords: Meir-Keeler-type
zbMATH Keywords: Thompson metric
zbMATH Keywords: \(\varepsilon \)-chainable
zbMATH Keywords: periodic boundary value problem
zbMATH Keywords: elastic beam equation
MaRDI profile type: Publication
full work available at URL: s12215-012-0089-z
OpenAlex ID: W2023620703
cites work: Fixed point theory and applications
cites work: Three positive fixed points of nonlinear operators on ordered Banach spaces
cites work: The upper and lower solution method for some fourth-order boundary value problems
cites work: On Nonlinear Contractions
cites work: A variant of the Meir-Keeler-type theorem in ordered Banach spaces
cites work: A Generalization of Banach's Contraction Principle
cites work: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces
cites work: Q5185568
cites work: Q4421936
cites work: An Extension of Banach's Contraction Principle
cites work: Existnence and nonexistence of positive solutions of fourth order nonlinear boundary value problems
cites work: Q3994493
cites work: Equivalent conditions and the Meir-Keeler type theorems
cites work: Equivalence of some contractivity properties over metrical structures
cites work: Remarks on first and second order periodic boundary value problems
cites work: Monotone method for second order periodic boundary value problems
cites work: A theorem on contraction mappings
cites work: Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
cites work: Nonlinear second order periodic value problems with caratheodory functions
cites work: Periodic boundary value problem for second order integro-ordinary differential equations with general kernel and Carathéodory nonlinearities
cites work: Hilbert’s projective metric and iterated nonlinear maps
cites work: Existence and multiplicity of positive solutions for an elastic beam equation
cites work: A Note on Contractive Mappings
cites work: A generalized Banach contraction principle that characterizes metric completeness
cites work: On Certain Contraction Mappings in a Partially Ordered Vector Space
cites work: On Branciari's theorem for weakly compatible mappings
cites work: Triple positive solutions of a class of fourth-order two-point boundary value problems
cites work: Positive solutions of nonlinear second-order periodic boundary value problems
cites work: Q3706042
cites work: A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations
DOI: 10.1007/S12215-012-0089-Z
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 6107836