On asymptotics of solutions for a class of functional differential inclusions

• Autorzy: Sergei Kornev , Valeri Obukhovskii , Jen-Chih Yao
• Języki publikacji: EN

Abstrakty

EN

We define a non-smooth guiding function for a functional differential inclusion and apply it to the study the asymptotic behavior of its solutions.

Słowa kluczowe

EN

asymptotic behavior; functional differential inclusion; integral guiding function; non-smooth guiding function

Kategorie tematyczne

• 34E05: Asymptotic expansions
• 34K09: Functional-differential inclusions
• 34C37: Homoclinic and heteroclinic solutions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2014
• Tom: 34
• Numer: 2
• Strony: 219-227

Daty

wydano

2014

otrzymano

2014-08-24

Twórcy

autor

Sergei Kornev

• Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 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] A.V. Arutyunov and V.I. Blagodatskikh, The maximum principle for differential inclusions with phase constraints, (Russian) Trudy Mat. Inst. Steklov 200 (1991) 4-26; translation in Proc. Steklov Inst. Math. 1993, no. 2 (200), 3-25.
• [2] A.V. Arutyunov, S.M. Aseev and V.I. Blagodatskikh, Necessary conditions of the first order in a problem of the optimal control of a differential inclusion with phase constraints, (Russian) Mat. Sb. 184 (6) (1993) 3-32; translation in Russian Acad. Sci. Sb. Math. 79 (1994), no. 1, 117-139.
• [3] J.-P. Aubin and A. Cellina, Differential Inclusions, Set-Valued Maps and Viability Theory, Grundlehren der Mathematischen Wissenschaften, 264 (Springer-Verlag, Berlin, 1984).
• [4] C. Avramescu, Asymptotic behavior of solutions of nonlinear differential equations and generalized guiding functions, Electronic Journal of Qualitive Theory of Differential Equations, no. 13 (2003) 1-9.
• [5] C. Avramescu, Existence problems for homoclinic solutions, Abstract and Applied Analysis 7 (1) (2002) 1-29. doi: 10.1155/S108533750200074X
• [6] C. Avramescu, Evanescent solutions of linear ordinary differential equations, Electronic Journal of Qualitive Theory of Differential Equations, no. 9 (2002) 1-12. doi: 10.1076/opep.9.1.1.1715
• [7] Yu.G. Borisovich, B.D. Gel'man, A.D. Myshkis and V.V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, (Russian) Librokom, Moscow, 2011.
• [8] F.H. Clarke, Optimization and Nonsmooth Analysis, Second edition, Classics in Applied Mathematics, 5, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990.
• [9] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Second edition. Topological Fixed Point Theory and Its Applications, 4 (Springer, Dordrecht, 2006).
• [10] 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, Berlin-New York, 2001).
• [11] N. Kikuchi, On control problems for functional-differential equations, Funkcial. Ekvac. 14 (1971) 1-23.
• [12] M. Kisielewicz, Differential Inclusions and Optimal Control (Kluwer, Dordrecht: PWN Polish Scientific Publishers, Warsaw, 1991).
• [13] S.V. Kornev and V.V. Obukhovskii, On nonsmooth multivalent guiding functions, (Russian) Differ. Uravn. 39 (11) (2003), 1497-1502, 1581; translation in Differ. Eq. 39 (11) (2003) 1578-1584.
• [14] S. Kornev and V. Obukhovskii, On some developments of the method of integral guiding functions, Functional Differ. Eq. 12 (3-4) (2005) 303-310.
• [15] M.A. Krasnosel'skii, The Operator of Translation Along the Trajectories of Differential Equations, Translations of Mathematical Monographs, Vol. 19 (American Mathematical Society, Providence, R.I., 1968).
• [16] M.A. Krasnosel'skii and A.I. Perov, On a certain principle of existence of bounded, periodic and almost periodic solutions of systems of ordinary differential equations, (Russian) Dokl. Akad. Nauk SSSR 123 (1958) 235-238.
• [17] V.V. Obukhovskii, Semilinear functional-differential inclusions in a Banach space and controlled parabolic systems, Soviet J. Automat. Inform. Sci. 24 (3) (1991) 71-79 (1992); translated from Avtomatika 1991, no. 3, 73-81.
• [18] V. Obukhovskii, P. Zecca, N.V. Loi and S. Kornev, Method of Guiding Functions in Problems of Nonlinear Analysis, Lecture Notes in Math. 2076 (Berlin, Springer, 2013).

Identyfikatory

DOI

10.7151/dmdico1165