Description

• Title:
  Filippov-Ważewski theorems and structure of solution sets for first order impulsive semilinear functional differential inclusions
• Creator:
  Djebali, Smaïl;
  Górniewicz, Lech;
  Ouahab, Abdelghani
• Description:
  In this paper, we first present an impulsive version of Filippov's Theorem for first-order semilinear functional differential inclusions of the form: $$ \cases (y'-Ay) \in F(t,y_t) &\text{a.e. } t\in J\setminus \{t_{1},\ldots,t_{m}\}, \\ y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})) &\text{for } k=1,\ldots,m, \\ y(t)=\phi(t) &\text{for } t\in[-r,0], \endcases $$ where $J=[0,b]$, $A$ is the infinitesimal generator of a $C_0$-semigroup on a separable Banach space $E$ and $F$ is a set-valued map. The functions $I_k$ characterize the jump of the solutions at impulse points $t_k$ ($k=1,\ldots,m$). Then the convexified problem is considered and a Filippov-Wa{\plr ż}ewski result is proved. Further to several existence results, the topological structure of solution sets -- closeness and compactness -- is also investigated. Some results from topological fixed point theory together with notions of measure on noncompactness are used. Finally, some geometric properties of solution sets, AR, $R_\delta$-contractibility and acyclicity, corresponding to Aronszajn-Browder-Gupta type results, are obtained.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2008.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 32, No 2 (December 2008); 261 - 312;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.049/8783
• Subject:
  Impulsive functional differential inclusions;
  mild solution;
  Filippov's theorem;
  relaxation;
  solution set;
  compactness;
  AR;
  $R_\delta$;
  contractibility;
  acyclicity;
  34A37;
  34A60;
  34K30;
  34K45;
  47D60;
  47H09;
  47H10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2008.049
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other