Description

• Title:
  Boundary value problems for first order systems on the half-line
• Creator:
  Rabier, Patric J.;
  Stuart, Charles A.
• Description:
  We prove existence theorems for first order boundary value problems on $(0,\infty)$, of the form $\dot{u}+F(\cdot,u)=f$, $Pu(0)=\xi$, where the function $F=F(t,u)$ has a $t$-independent limit $F^{\infty}(u)$ at infinity and $P$ is a given projection. The right-hand side $f$ is in $L^{p} ((0,\infty),{\mathbb R}^{N})$ and the solutions $u$ are sought in $W^{1,p}((0,\infty),{\mathbb R}^{N})$, so that they tend to $0$ at infinity. By using a degree for Fredholm mappings of index zero, we reduce the existence question to finding {\it a priori} bounds for the solutions. Nevertheless, when the right-hand side has exponential decay, our existence results are valid even when the governing operator is not Fredholm.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2005.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 25, No 1 (March 2005); 101 - 131;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.005/9257
• Subject:
  Ordinary differential equation;
  half-line;
  Sobolev space;
  boundary and initial value problem;
  Fredholm operator;
  a-priori bounds;
  43A12;
  34B15;
  47A53;
  47H11
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2005.005
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other