Description

• Title:
  Heteroclinic solutions between stationary points at different energy levels
• Creator:
  Coti Zelati, Vittorio;
  Rabinowitz, Paul H.
• Description:
  Consider the system of equations $$ -\ddot{q} = a(t)V'(q). $$ The main goal of this paper is to present a simple minimization method to find heteroclinic connections between isolated critical points of $V$, say $0$ and $\xi$, which are local maxima but do not necessarily have the same value of $V$. In particular we prove that there exist heteroclinic solutions from $0$ to $\xi$ and from $\xi$ to $0$ for a class of positive slowly oscillating periodic functions $a$ provided $\delta = |V(0) - V(\xi)|$ is sufficiently small (and another technical condition is satisfied). Note that when $V(0) \neq V(\xi)$, $a$ cannot be constant be conservation of energy. Existence of ``multi-bump'' solutions is also proved.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2001.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 17, No 1 (March 2001); 1 - 21;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.001/9952
• Subject:
  Heteroclinic solutions;
  variational methods;
  Lagrangian systems;
  37J45;
  34C37;
  37C29;
  70K44
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.001
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other