Nontrivial application of Nielsen theory to differential systems
type: Item
instance of: scholarly article
title: Nontrivial application of Nielsen theory to differential systems
zbMATH Open document ID: 1113.34006
author: Jan Andres
author: Tomáš Fürst
published in: Journal of Differential Equations
publication date: 2007-01-16T00:00:00Z
review text: Nielsen theory is one of the few fixed point theories dealing with more than one fixed point. It allows us to obtain a lower estimate for the number of fixed points. The nontrivial application of this theory to differential equations is considered to be a difficult task. The main purpose of this paper is to present a nontrivial example of an application of Nielsen's fixed point theory to a planar system of differential inclusion which has at least two periodic solutions.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5116261
zbMATH Keywords: Nielsen number
zbMATH Keywords: lower estimate of solutions
zbMATH Keywords: nontrivial example
zbMATH Keywords: three periodic solutions
zbMATH Keywords: no subdomain
MaRDI profile type: Publication
full work available at URL: j.jde.2006.05.016
OpenAlex ID: W2003762182
cites work: Multiple bounded solutions of differential inclusions: The Nielsen theory approach
cites work: A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray
cites work: Nielsen number and differential equations
cites work: Q5694116
cites work: An example of application of the Nielsen theory to integro-differential equations
cites work: Q4423184
cites work: Q3324260
cites work: A generalized Nielsen number and multiplicity results for differential inclusions
cites work: Q5532996
cites work: Q3831547
cites work: Q3816377
cites work: Topological identification of multiple solutions to parametrized nonlinear equations
cites work: Q5694109
cites work: Multiple local solutions to nonlinear control processes
cites work: Isolating segments for Carathéodory systems and existence of periodic solutions
cites work: Q4285964
cites work: Nielsen fixed point theory and nonlinear equations
cites work: Differential Equations with Nonlinear Boundary Conditions
cites work: Multiple periodic solutions of small vector fields on differentiable manifolds
cites work: Parametrized singular boundary value problems
cites work: Multiple solutions of nonlinear equations via Nielsen fixed-point theory: A survey
cites work: Q4421936
cites work: Lectures on Nielsen fixed point theory
cites work: The number and linking of periodic solutions of periodic systems
cites work: Waveform in the dynamical study of ordinary differential equations
cites work: The number of linking of periodic solutions of nondissipative systems
cites work: Q4842674
cites work: Q4934442
DOI: 10.1016/J.JDE.2006.05.016
Recommended article: Q3816377
Recommended article: Nielsen fixed point theory and nonlinear equations
Recommended article: A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray
Recommended article: Q4941072
Recommended article: An example of application of the Nielsen theory to integro-differential equations
Recommended article: Q4581789
Recommended article: Nielsen number and differential equations
Recommended article: Q4278142
Recommended article: Q4233712
Recommended article: Linked dichotomies and asymptotic theory of nondiagonal differential systems
description: scientific article; zbMATH DE number 5116261