On the topological dimension of the solutions sets for some classes of operator and differential inclusions

Ralf Bader; Boris D. Gel'man; Mikhail Kamenskii; Valeri Obukhovskii

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2002)

  • Volume: 22, Issue: 1, page 17-32
  • ISSN: 1509-9407

Abstract

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In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form = S F where F is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.

How to cite

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Ralf Bader, et al. "On the topological dimension of the solutions sets for some classes of operator and differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 22.1 (2002): 17-32. <http://eudml.org/doc/271523>.

@article{RalfBader2002,
abstract = {In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $ = S _F$ where $_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.},
author = {Ralf Bader, Boris D. Gel'man, Mikhail Kamenskii, Valeri Obukhovskii},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {solutions set; fixed points set; topological dimension; multivalued map; condensing map; topological degree; differential inclusion; periodic problem; fixed point; condensing mapping; multivalued mapping},
language = {eng},
number = {1},
pages = {17-32},
title = {On the topological dimension of the solutions sets for some classes of operator and differential inclusions},
url = {http://eudml.org/doc/271523},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Ralf Bader
AU - Boris D. Gel'man
AU - Mikhail Kamenskii
AU - Valeri Obukhovskii
TI - On the topological dimension of the solutions sets for some classes of operator and differential inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2002
VL - 22
IS - 1
SP - 17
EP - 32
AB - In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $ = S _F$ where $_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.
LA - eng
KW - solutions set; fixed points set; topological dimension; multivalued map; condensing map; topological degree; differential inclusion; periodic problem; fixed point; condensing mapping; multivalued mapping
UR - http://eudml.org/doc/271523
ER -

References

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