Description

• 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:
  free access
• 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:
  English
• 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
• Can I use it?:
  seek permission
• Type:
  other