Topological properties of the solution set of integrodifferential inclusions

Evgenios P. Avgerinos; Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 429-442
  • ISSN: 0010-2628

Abstract

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In this paper we examine nonlinear integrodifferential inclusions in ℝ N . For the nonconvex problem, we show that the solution set is a retract of the Sobolev space W 1 , 1 ( T , ℝ N ) and the retraction can be chosen to depend continuously on a parameter λ . Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retract of C ( T , ℝ N ) . Finally we prove some continuous dependence results.

How to cite

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Avgerinos, Evgenios P., and Papageorgiou, Nikolaos S.. "Topological properties of the solution set of integrodifferential inclusions." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 429-442. <http://eudml.org/doc/247749>.

@article{Avgerinos1995,
abstract = {In this paper we examine nonlinear integrodifferential inclusions in $\mathbb \{R\}^N$. For the nonconvex problem, we show that the solution set is a retract of the Sobolev space $W^\{1,1\}(T,\{\mathbb \{R\}^N\})$ and the retraction can be chosen to depend continuously on a parameter $\lambda $. Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retract of $C(T,\{\mathbb \{R\}^N\})$. Finally we prove some continuous dependence results.},
author = {Avgerinos, Evgenios P., Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {retract; absolute retract; path-connected; Vietoris continuous; $h$-continuous; orientor field; integrodifferential inclusion; retract; continuous selector},
language = {eng},
number = {3},
pages = {429-442},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Topological properties of the solution set of integrodifferential inclusions},
url = {http://eudml.org/doc/247749},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Avgerinos, Evgenios P.
AU - Papageorgiou, Nikolaos S.
TI - Topological properties of the solution set of integrodifferential inclusions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 429
EP - 442
AB - In this paper we examine nonlinear integrodifferential inclusions in $\mathbb {R}^N$. For the nonconvex problem, we show that the solution set is a retract of the Sobolev space $W^{1,1}(T,{\mathbb {R}^N})$ and the retraction can be chosen to depend continuously on a parameter $\lambda $. Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retract of $C(T,{\mathbb {R}^N})$. Finally we prove some continuous dependence results.
LA - eng
KW - retract; absolute retract; path-connected; Vietoris continuous; $h$-continuous; orientor field; integrodifferential inclusion; retract; continuous selector
UR - http://eudml.org/doc/247749
ER -

References

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