Topological properties of the solution set of a class of nonlinear evolutions inclusions

Nikolaos S. Papageorgiou

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 3, page 409-424
  • ISSN: 0011-4642

Abstract

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In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F ( t , x ) , we are able to show that the solution set is in fact an R δ -set. Finally some applications to infinite dimensional control systems are also presented.

How to cite

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Papageorgiou, Nikolaos S.. "Topological properties of the solution set of a class of nonlinear evolutions inclusions." Czechoslovak Mathematical Journal 47.3 (1997): 409-424. <http://eudml.org/doc/30372>.

@article{Papageorgiou1997,
abstract = {In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field $F(t,x)$, we are able to show that the solution set is in fact an $R_\delta $-set. Finally some applications to infinite dimensional control systems are also presented.},
author = {Papageorgiou, Nikolaos S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {$R_\delta $-set; homotopic; contractible; evolution triple; evolution inclusion; compact embedding; optimal control; infinite-dimensional control systems},
language = {eng},
number = {3},
pages = {409-424},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Topological properties of the solution set of a class of nonlinear evolutions inclusions},
url = {http://eudml.org/doc/30372},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
TI - Topological properties of the solution set of a class of nonlinear evolutions inclusions
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 409
EP - 424
AB - In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field $F(t,x)$, we are able to show that the solution set is in fact an $R_\delta $-set. Finally some applications to infinite dimensional control systems are also presented.
LA - eng
KW - $R_\delta $-set; homotopic; contractible; evolution triple; evolution inclusion; compact embedding; optimal control; infinite-dimensional control systems
UR - http://eudml.org/doc/30372
ER -

References

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