Description

• Title:
  Some existence results for dynamical systems on non-complete Riemannian manifolds
• Creator:
  Mirenghi, Elvira;
  Tucci, Maria
• Description:
  Let $\mathcal M^*$ be a non-complete Riemannian manifold with bound-ed topological boundary and $V: \mathcal M \to \mathbb R$ a $C^2$ potential function subquadratic at infinity. In this paper we look for curves $x: [0,T]\to\mathcal M$ having prescribed period $T$ or joining two fixed points of $\mathcal M$, satisfying the system $$ D_t (\dot x(t))=-\nabla_R V(x(t)), $$ where $D_t(\dot x(t))$ is the covariant derivative of $\dot x$ along the direction of $\dot x$ and $\nabla_R V$ the Riemannian gradient of $V$. We assume that $V(x) \to -\infty$ if $d(x,\partial\mathcal M)\to 0$ and, in the periodic case, suitable hypotheses on the sectional curvature of $\mathcal M$ at infinity. We use variational methods in addition with a penalization technique and Morse index estimates.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  1999.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 13, No 1 (March 1999); 163 - 180;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.008/10050
• Subject:
  Variational methods;
  Riemannian manifold;
  Morse index;
  sectional curvature;
  58EXX;
  58E05;
  58FXX
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.008
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other