Description

• Title:
  Existence, localization and stability of limit-periodic solutions to differential equations involving cubic nonlinearities
• Creator:
  Andres, Jan;
  Pennequin, Denis
• Description:
  We will prove, besides other things like localization and (in)stability, that the differential equations $x'+x^3-\lambda x=\varepsilon r(t)$, $\lambda> 0$, and $x''+x^3-x=\varepsilon r(t)$, where $r\colon\mathbb{R}\to\mathbb{R}$ are uniformly limit-periodic functions, possess for sufficiently small values of $\varepsilon > 0$ uniformly limit-periodic solutions, provided $r$ in the first-order equation is strictly positive. As far as we know, these are the first nontrivial effective criteria, obtained for limit-periodic solutions of nonlinear differential equations, in the lack of global lipschitzianity restrictions. A simple illustrative example is also indicated for difference equations.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.13
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2B (December 2019); 887 - 906;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031/17999 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031/18000
• Subject:
  Limit-periodic solutions;
  differential equations;
  cubic nonlinearity;
  existence of solutions;
  localization;
  (in)stability;
  essentiality;
  34C15;
  34C27;
  34K14
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other