Description

• Title:
  An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems
• Creator:
  Janczewska, Joanna
• Description:
  In this work the problem of the existence of almost homoclinic solutions for a Newtonian system $\ddot{q}+V_{q}(t,q)=f(t)$, where $t\in\mathbb R$ and $q\in\mathbb R^n$, is considered. It is assumed that a potential $V\colon\mathbb R\times\mathbb R^{n}\to\mathbb R$ is $C^{1}$-smooth with respect to all variables and $T$-periodic in a time variable $t$. Moreover, $f\colon\mathbb R\to\mathbb R^{n}$ is a continuous bounded square integrable function and $f\neq 0$. This system may not have a trivial solution. However, we show that under some additional conditions there exists a solution emanating from $0$ and terminating to $0$. We are to call such a solution almost homoclinic to $0$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2009.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 33, No 1 (March 2009); 169 - 177;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.012/8651
• Subject:
  Almost homoclinic solution;
  periodic orbit;
  action functional;
  Newtonian system;
  37J45;
  58E05;
  34C37;
  70H05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2009.012
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other