# 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

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topMikhail 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

top- [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] 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] 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] 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] 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] 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] 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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