Description

• Title:
  Differential inclusions with nonlocal conditions: existence results and topological properties of solution sets
• Creator:
  Graef, John R.;
  Henderson, Johnny;
  Ouahab, Abdelghani
• Description:
  In this paper, we study the topological structure of solution sets for the first-order differential inclusions with nonlocal conditions: $$ \cases y'(t) \in F(t,y(t)) &\text{a.e } t\in [0,b],\\ y(0)+g(y)=y_0, \endcases $$ where $F\colon [0,b]\times \mathbb{R}^n\to{\mathcal P}(\mathbb{R}^n)$ is a multivalued map. Also, some geometric properties of solution sets, $R_{\delta}$, $R_\delta$-contractibility and acyclicity, corresponding to Aronszajn-Browder-Gupta type results, are obtained. Finally, we present the existence of viable solutions of differential inclusions with nonlocal conditions and we investigate the topological properties of the set constituted by these solutions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2011.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 37, No 1 (March 2011); 117 - 145;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.006/8396
• Subject:
  Differential inclusions;
  nonlocal conditions;
  solution set;
  compactness;
  $R_{\delta}$;
  $R_\delta$-contractibility;
  acyclicity;
  proximate retract;
  tangential conditions;
  viable solutions;
  34A37;
  34A60;
  34K30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.006
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other