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2001 | 21 | 2 | 261-282
Tytuł artykułu

Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we shall establish sufficient conditions for the controllability on semi-infinite intervals for first and second order functional differential inclusions in Banach spaces. We shall rely on a fixed point theorem due to Ma, which is an extension on locally convex topological spaces, of Schaefer's theorem. Moreover, by using the fixed point index arguments the implicit case is treated.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
21
Numer
2
Strony
261-282
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-12-05
Twórcy
  • Department of Mathematics, University of Sidi Bel Abbes, BP 89, 22000 Sidi Bel Abbes, Algeria
  • Faculty of Mathematic and Informatic Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
  • Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
Bibliografia
  • [1] K. Balachandran, P. Balasubramaniam and J.P. Dauer, Controllability of nonlinear integrodifferential systems in Banach space, J. Optim. Theory Appl. 84 (1995), 83-91.
  • [2] K. Balachandran, P. Balasubramaniam and J.P. Dauer, Local null controllability of nonlinear functional differential systems in Banach space, J. Optim. Theory Appl. 75 (1996), 61-75.
  • [3] M. Benchohra and S.K. Ntouyas, Controllability for functional differential and integrodifferential inclusions in Banach spaces, submitted.
  • [4] N. Carmichael and M.D. Quinn, An approash to nonlinear control problems using fixed point methods, degree theory and pseudo-inverses, Numerical Functional Analysis and Optimization 7 (1984-1985), 197-219.
  • [5] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York 1990.
  • [6] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin - New York 1992.
  • [7] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mat. PWN, Warsaw 1982.
  • [8] H.O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
  • [9] H.O. Fattorini, Ordinary differential equations in linear topological spaces, II, J. Differential Equations 6 (1969), 50-70.
  • [10] J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York 1985.
  • [11] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht 1999.
  • [12] L. Górniewicz, P. Nistri and V. Obukhovskii, Differential inclusions on proximate retracts of Hilbert spaces, International J. Nonlin. Diff. Eqn. TMA, 3 (1997), 13-26.
  • [13] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York 1994.
  • [14] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London 1997.
  • [15] A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
  • [16] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Diss. Math. 92 (1972), 1-43.
  • [17] M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 4 (3) (1975), 70-76.
  • [18] C.C. Travis and G.F. Webb, Second order differential equations in Banach spaces, Proc. Int. Symp. on Nonlinear Equations in Abstract Spaces, Academic Press, New York (1978), 331-361.
  • [19] C.C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungar. 32 (1978), 75-96.
  • [20] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1028
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