ArticleOriginal scientific text
Title
On some topological methods in theory of neutral type operator differential inclusions with applications to control systems
Authors 1, 2, 3, 4
Affiliations
- Faculty of Mathematics, Voronezh State University, 394006 Voronezh, Russia
- Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia
- Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan
- Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
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.
Keywords
operator differential inclusion, neutral type, periodic solution, fixed point, multivalued map, condensing map, topological degree, averaging method, control system, distributed control
Bibliography
- 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
- 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.
- L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, 2nd edition, Topological Fixed Point Theory and Its Applications, 4. Springer, Dordrecht, 2006.
- S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I. Theory, Mathematics and its Applications, 419. Kluwer Academic Publishers, Dordrecht, 1997.
- 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
- 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.
- 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.
Pages:
193-204
Main language of publication
English
Received
2013-08-07
Published
2013
DOI: 10.7151/dmdico1152
Exact and natural sciences