Description

• Title:
  Almost homoclinic solutions for the second order Hamiltonian systems
• Creator:
  Janczewska, Joanna
• Description:
  The second order Hamiltonian system $\ddot{q}+V_{q}(t,q)=f(t)$, where $t\in\mathbb R$ and $q\in\mathbb R^n$, is considered. We assume that a potential $V\in C^{1}(\mathbb R\times\mathbb R^n,\mathbb R)$ is of the form $V(t,q)=-K(t,q)+W(t,q)$, where $K$ satisfies the pinching condition and $W_{q}(t,q)=o(|q|)$, as $|q|\to 0$ uniformly with respect to $t$. It is also assumed that $f\in C(\mathbb R,\mathbb R^n)$ is non-zero and sufficiently small in $L^{2}(\mathbb R,\mathbb R^n)$. In this case $q\equiv 0$ is not a solution. Therefore there are no orbits homoclinic to $0$ in a classical sense. However, we show that there is a solution emanating from $0$ and terminating at $0$. We are to call such a solution almost homoclinic to $0$. It is obtained here as a weak limit in $W^{1,2}(\mathbb R,\mathbb R^n)$ of a sequence of almost critical points.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2008.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 32, No 1 (September 2008); 131 - 137;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.040/8797
• Subject:
  Action functional;
  almost homoclinic solution;
  Hamiltonian system;
  37J45;
  58E05;
  34C37;
  70H05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.040
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other