Description

• Title:
  Computer-assisted proof of a periodic solution in a nonlinear feedback DDE
• Creator:
  Zalewski, Mikołaj
• Description:
  In this paper, we rigorously prove the existence of a non-trivial periodic orbit for the nonlinear DDE: $x'(t) = - K \sin(x(t-1))$ for $K=1.6$. We show that the equations for the Fourier coefficients have a solution by computing the local Brouwer degree. This degree can be computed by using a homotopy, and its validity can be proved by checking a finite number of inequalities. Checking these inequalities is done by a computer program.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 2 (June 2009); 373 - 393;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.025/8633
• Subject:
  Topological degree;
  dynamical systems;
  ordinary differential equations;
  55M20;
  34K15;
  34C35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.025
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other