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

Mouffak Benchohra; Lech Górniewicz; Sotiris K. Ntouyas

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

  • Volume: 21, Issue: 2, page 261-282
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Mouffak Benchohra, Lech Górniewicz, and Sotiris K. Ntouyas. "Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.2 (2001): 261-282. <http://eudml.org/doc/271528>.

@article{MouffakBenchohra2001,
abstract = {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.},
author = {Mouffak Benchohra, Lech Górniewicz, Sotiris K. Ntouyas},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {controllability; mild solution; evolution; fixed point; functional differential inclusions; fixed point theorem},
language = {eng},
number = {2},
pages = {261-282},
title = {Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces},
url = {http://eudml.org/doc/271528},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Mouffak Benchohra
AU - Lech Górniewicz
AU - Sotiris K. Ntouyas
TI - Controllability on infinite time horizon for first and second order functional differential inclusions in Banach spaces
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 2
SP - 261
EP - 282
AB - 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.
LA - eng
KW - controllability; mild solution; evolution; fixed point; functional differential inclusions; fixed point theorem
UR - http://eudml.org/doc/271528
ER -

References

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  1. [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. Zbl0821.93010
  2. [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. Zbl0848.93007
  3. [3] M. Benchohra and S.K. Ntouyas, Controllability for functional differential and integrodifferential inclusions in Banach spaces, submitted. Zbl1020.93002
  4. [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. Zbl0563.93013
  5. [5] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York 1990. 
  6. [6] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin - New York 1992. 
  7. [7] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mat. PWN, Warsaw 1982. 
  8. [8] H.O. Fattorini, Ordinary differential equations in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105. Zbl0175.15101
  9. [9] H.O. Fattorini, Ordinary differential equations in linear topological spaces, II, J. Differential Equations 6 (1969), 50-70. Zbl0181.42801
  10. [10] J.A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, New York 1985. Zbl0592.47034
  11. [11] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht 1999. Zbl0937.55001
  12. [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. [13] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York 1994. Zbl0804.34001
  14. [14] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London 1997. Zbl0887.47001
  15. [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. Zbl0151.10703
  16. [16] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Diss. Math. 92 (1972), 1-43. 
  17. [17] M. Martelli, A Rothe's type theorem for non-compact acyclic-valued map, Boll. Un. Mat. Ital. 4 (3) (1975), 70-76. Zbl0314.47035
  18. [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. Zbl0455.34044
  19. [19] C.C. Travis and G.F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Hungar. 32 (1978), 75-96. Zbl0388.34039
  20. [20] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin 1980. 

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