Description

• Title:
  Multiple solutions with prescribed minimal period for second order odd Newtonian systems with symmetries
• Creator:
  Krawcewicz, Wiesław;
  Lv, Yanli;
  Xiao, Huafeng
• Description:
  For an orthogonal $\Gamma$-representation $V$ ($\Gamma$ is a finite group) and for an even $\Gamma$-invariant $C^2$-functional $f\colon V\to \mathbb R$ satisfying the condition $0\lt \theta \nabla f(x)\bullet x\le \nabla^2 f(x)x\bullet x$ (for $\theta\gt 1$ and $x\in V\setminus \{0\}$), we consider the odd Newtonian system $\ddot x(t)=-\nabla f(x(t))$ and establish the existence of multiple periodic solutions with a minimal period $p$ (for any given $p\gt 0$). As an example, we prove the existence of arbitrarily many periodic solutions with minimal period $p$ for a specific $D_n$-symmetric Newtonian system.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 47, No 2 (June 2016); 659 - 679;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.024/8059 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.024/8060
• Subject:
  Periodic solutions;
  Nehari manifold;
  Palais-Smale condition;
  H-fixed-point reduction;
  34K13;
  58E50
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.024
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other