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On asymptotics of solutions for a class of functional differential inclusions

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We define a non-smooth guiding function for a functional differential inclusion and apply it to the study the asymptotic behavior of its solutions.
  • Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 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
  • [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.
  • [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).
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