Description

• Title:
  On solutions of two-point boundary value problems inside isolating segments
• Creator:
  Srzednicki, Roman
• Description:
  We consider a two-point boundary value problem $$ \dot x=f(t,x), \quad x(a)=g(x(b)). $$ We assume that in the extended space of the equation there exist an isolating segment, a set such that $f$ properly behaves on its boundary. We give a formula for the fixed point index of the composition of $g$ with the translation operator in a neighbourhood of the set of the initial points of solutions contained in the isolating segment. We apply that formula to results on existence of solutions of some planar boundary value problem associated to equations of the form $\dot z=\overline z^q+\ldots$ and $\dot z=e^{it}\overline z^q+\ldots$.
• 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); 73 - 89;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.004/10046
• Subject:
  Boundary value problem;
  isolating segment;
  Lefschetz number;
  fixed point index;
  Primary 34B15;
  Secondary 54H20;
  55M20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.1999.004
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other