Szczegóły obiektu: Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case

Instytucja dostarczająca:Akademicka Platforma Czasopism

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Title:
Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case
Creator:
Couchouron, Jean-Francois;
Kamenskii, Mikhail I.;
Mikhaylenko, Boris;
Nistri, Paolo
Description:
We consider a $T$-periodically perturbed autonomous functional differential equation of neutral type. We assume the existence of a $T$-periodic limit cycle $x_0$ for the unperturbed autonomous system. We also assume that the linearized unperturbed equation around the limit cycle has the characteristic multiplier $1$ of geometric multiplicity $1$ and algebraic multiplicity greater than~$1$. The paper deals with the existence of a branch of $T$-periodic solutions emanating from the limit cycle. The problem of finding such a branch is converted into the problem of finding a branch of zeros of a~suitably defined bifurcation equation \hbox{$P(x,\varepsilon) +\varepsilon Q(x, \varepsilon)=0$.} The main task of the paper is to define a novel equivalent integral operator having the property that the $T$-periodic adjoint Floquet solutions of the unperturbed linearized operator correspond to those of the equation $P'(x_0(\theta),0)=0$, $\theta\in[0,T]$. Once this is done it is possible to express the condition for the existence of a branch of zeros for the bifurcation equation in terms of a multidimensional Malkin bifurcation function.
Object availability:
Dostęp otwarty
Rights:
Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
Date:
2015.12.01
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
angielski
Source:
Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 631 - 664;
1230-3429
Format:
application/pdf
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.062/7236 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.062/7237
Subject:
Neutral functional differential equations;
periodic perturbations;
adjoint Floquet solutions;
periodic bifurcation;
multidimensional Malkin bifurcation function;
Primary;
34K40;
34K27;
34K18;
34K13;
Secondary;
47G10;
47H08
Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.062
Data provider:
Akademicka Platforma Czasopism

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Szczegóły obiektu: Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case

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