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2007 | 27 | 2 | 329-347
Tytuł artykułu

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

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EN
Abstrakty
EN
In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.
Twórcy
autor
  • Département de Mathématiques, Université Mentouri de Constantine, Algérie
  • Department of Mathematics, University of Sidi Bel Abbès, PO Box 89, 22000 Sidi Bel Abbès, Algeria
  • Département de Mathématiques, Universit Kasdi Merbah de Ouargla, Alégrie
  • Department of Mathematics, University of Sidi Bel Abbès, PO Box 89, 22000 Sidi Bel Abbès, Algeria
Bibliografia
  • [1] N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics Series, 246. Longman Scientific & Technical, Harlow John Wiley & Sons, Inc., New York, 1991.
  • [2] H. Amann, Linear and Quasilinear Parabolic Problems, Birkhäuser, Berlin, 1995.
  • [3] B. Amir and L. Maniar, Application de la théorie d'extrapolation pour la résolution des équations différentielles à retard homogènes, Extracta Math. 13 (1998), 95-105.
  • [4] B. Amir and L. Maniar, Composition of pseudo almost periodic functions and Cauchy problems with operator of nondense domain, Ann. Math. Blaise Pascal 6 (1999), 1-11.
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  • [6] M. Benchohra, L. Górniewicz, S.K. Ntouyas and A. Ouahab, Controllability results for impulsive functional differential inclusions, Rep. Math. Phys. 54 (2004), 211-227.
  • [7] M. Benchohra, L. Górniewicz, S.K. Ntouyas and A. Ouahab, Existence results for nondensely defined impulsive semilinear functional differential equations, Nonlinear Analysis and Applications, edited by R.P. Agarwal and D. O'Regan, Kluwer, 2003.
  • [8] M. Benchohra, J. Henderson and S.K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, Vol. 2, New York, 2006.
  • [9] M. Benchohra and A. Ouahab, Controllability results for functional semilinear differential inclusions in Fréchet spaces, Nonlinear Anal. 61 (2005), 405-423.
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  • [14] E.P. Gatsori, L. Górniewicz and S.K. Ntouyas, Controllability results for nondensely defined evolution impulsive differential inclusions with nonlocal conditions, Panamer. Math. J. 15 (2) (2005), 1-27.
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  • [16] J. Henderson and A. Ouahab, Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces, Electron. J. Qual. Theory Differ. Equ. (2005), (11), 1-17.
  • [17] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991.
  • [18] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  • [19] A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser Verlag, 1995.
  • [20] L. Maniar and A. Rhandi, Extrapolation and inhomogeneous retarded differential equations on infinite-dimensional spaces, Circ. Mat. Palermo 47 (2) (1998), 331-346.
  • [21] R. Nagel and E. Sinestrari, Inhomogeneous Volterra Integrodifferential Equations for Hille-Yosida operators, In Functional Analysis, edited by K.D. Bierstedt, A. Pietsch, W.M. Ruess and D. Voigt, 51-70, Marcel Dekker, 1998.
  • [22] J. Neerven, The Adjoint of a Semigroup of Linear Operators, Lecture Notes in Math. 1529, Springer-Verlag, New York, 1992.
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  • [25] A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1088
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