Description

• Title:
  Schauder's Theorem and the method of a priori bounds
• Creator:
  Granas, Andrzej;
  Frigon, Marlène
• Description:
  We first recall simple proofs relying on the Schauder Fixed Point Theorem of the Nonlinear Alternative, the Leray-Schauder Alternative and the Coincidence Alternative for compact maps on normed spaces. We present also an alternative for compact maps defined on convex subsets of normed spaces. Those alternatives permit to apply the method of a priori bounds to obtain results establishing the existence of solutions to differential equations. Using those alternatives, we present some new proofs of existence results for first order differential equations.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.03.18
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 1 (September 2018); 99 - 109;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.053/14350 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.053/14351
• Subject:
  Fixed point;
  nonlinear alternative;
  Leray-Schauder alternative;
  Schauder fixed point theorem;
  coincidence;
  a priori bounds;
  differential equation;
  Primary;
  47H10;
  Secondary;
  54H25;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.053
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other