On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Mikhail Kamenskii; Valeri Obukhovskii; Jen-Chih Yao

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

  • Volume: 33, Issue: 2, page 193-204
  • ISSN: 1509-9407

Abstract

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We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.

How to cite

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Mikhail Kamenskii, Valeri Obukhovskii, and Jen-Chih Yao. "On some topological methods in theory of neutral type operator differential inclusions with applications to control systems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.2 (2013): 193-204. <http://eudml.org/doc/270542>.

@article{MikhailKamenskii2013,
abstract = {We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.},
author = {Mikhail Kamenskii, Valeri Obukhovskii, Jen-Chih Yao},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {operator differential inclusion; neutral type; periodic solution; fixed point; multivalued map; condensing map; topological degree; averaging method; control system; distributed control},
language = {eng},
number = {2},
pages = {193-204},
title = {On some topological methods in theory of neutral type operator differential inclusions with applications to control systems},
url = {http://eudml.org/doc/270542},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Mikhail Kamenskii
AU - Valeri Obukhovskii
AU - Jen-Chih Yao
TI - On some topological methods in theory of neutral type operator differential inclusions with applications to control systems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 2
SP - 193
EP - 204
AB - We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.
LA - eng
KW - operator differential inclusion; neutral type; periodic solution; fixed point; multivalued map; condensing map; topological degree; averaging method; control system; distributed control
UR - http://eudml.org/doc/270542
ER -

References

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  1. [1] Yu.G. Borisovich, B.D. Gelman, A.D. Myshkis and V.V. Obukhovskii, Topological methods in the theory of fixed points of multivalued mappings. (Russian) Uspekhi Mat. Nauk 35 (1980), 59-126. English translation: Russian Math. Surveys 35 (1980), 65-143. doi: 10.1070/RM1980v035n01ABEH001548 
  2. [2] Yu.G. Borisovich, B.D. Gelman, A.D. Myshkis and V.V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, (Russian) Second edition, Librokom, Moscow, 2011. 
  3. [3] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, 2nd edition, Topological Fixed Point Theory and Its Applications, 4. Springer, Dordrecht, 2006. Zbl1107.55001
  4. [4] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I. Theory, Mathematics and its Applications, 419. Kluwer Academic Publishers, Dordrecht, 1997. Zbl0887.47001
  5. [5] M. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, de Gruyter Series in Nonlinear Analysis and Applications, 7. Walter de Gruyter & Co., Berlin, 2001. doi: 10.1515/9783110870893 Zbl0988.34001
  6. [6] M.A. Krasnosel'skii and P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis, A Series of Comprehensive Studies in Mathematics, 263, Springer-Verlag, Berlin-Heidelberg-New York-Tokio, 1984. 
  7. [7] M.A. Krasnoselskii, P.P. Zabreiko, E.I. Pustyl'nik and P.E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoff International Publishing, Leyden, 1976. 

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