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

• Autorzy: Mikhail Kamenskii , Valeri Obukhovskii , Jen-Chih Yao
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

operator differential inclusion; neutral type; periodic solution; fixed point; multivalued map; condensing map; topological degree; averaging method; control system; distributed control

Kategorie tematyczne

• 47H08: Measures of noncompactness and condensing mappings, K -set contractions, etc.
• 47H05: Monotone operators and generalizations
• 34K09: Functional-differential inclusions
• 34K35: Control problems
• 47H11: Degree theory
• 34K13: Periodic solutions
• 34C29: Averaging method
• 34K40: Neutral equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2013
• Tom: 33
• Numer: 2
• Strony: 193-204

Daty

wydano

2013

otrzymano

2013-08-07

Twórcy

autor

Mikhail Kamenskii

• Faculty of Mathematics, Voronezh State University, 394006 Voronezh, Russia

autor

Valeri Obukhovskii

• Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia

autor

Jen-Chih Yao

• Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan
• Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Bibliografia

• [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.
• [4] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I. Theory, Mathematics and its Applications, 419. Kluwer Academic Publishers, Dordrecht, 1997.
• [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
• [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.

Identyfikatory

DOI

10.7151/dmdico1152