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ArticleOriginal scientific text

Title

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

Authors 1, 2, 2, 2

Affiliations

  1. Technical University Muenchen, D-80290 Muenchen, Germany
  2. Department of Mathematics, Voronezh University, (394693) Voronezh, Russia

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 =SF 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.

Keywords

ENG
solutions set, fixed points set, topological dimension, multivalued map, condensing map, topological degree, differential inclusion, periodic problem

Bibliography

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2002/22/1
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Pages:
17-32
Main language of publication
English
Received
2001-03-19
Published
2002

DOI: 10.7151/dmgt.1030

Exact and natural sciences