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Tytuł artykułu

On initial value problems for a class of first order impulsive differential inclusions

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Abstrakty
EN
We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.
Twórcy
  • Department of Mathematics, University of Sidi Bel Abbes, BP 89, 22000 Sidi Bel Abbes, Algeria
  • Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, B.O. Box 5046 Dhahran 31261, Saudi Arabia
  • Department of Mathematical Analysis, University de Santiago de Compostela, Santiago de Compostela 15706 A Coruña, Spain
Bibliografia
  • [1] J.P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston 1990.
  • [2] J.M. Ayerbe, T. Dominguez and G. Lopez-Acebo, Measure of Noncompactness in Metric Fixed Point Theory, Birkhäuser, Basel 1997.
  • [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York 1980.
  • [4] M. Benchohra and A. Boucherif, On first order initial value problems for impulsive differential inclusions in Banach Spaces, Dyn. Syst. Appl. 8 (1) (1999), 119-126.
  • [5] M. Benchohra and A. Boucherif, Initial Value Problems for Impulsive Differential Inclusions of First Order, Diff. Eq. and Dynamical Systems 8 (1) (2000), 51-66.
  • [6] K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992.
  • [7] L. Erbe and W. Krawcewicz, Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rockey Mountain J. Math. 22 (1992), 519-539.
  • [8] D. Franco, Problemas de frontera para ecuaciones diferenciales con impulsos, Ph.D Thesis, Univ. Santiago de Compostela (Spain), 2000 (in Spanish).
  • [9] M. Frigon and D. O'Regan, Existence results for first order impulsive differential equations, J. Math. Anal. Appl. 193, (1995), 96-113.
  • [10] M. Frigon and D. O'Regan, Boundary value problems for second order impulsive differential equations using set-valued maps, Rapport DMS-357, University of Montreal 1993.
  • [11] M. Frigon and D. O'Regan, First order impulsive initial and periodic value problems with variable moments, J. Math. Anal. Appl. 233 (1999), 730-739.
  • [12] M. Frigon, Application de la théorie de la transversalité topologique à des problèmes non linéaires pour des équations différentielles ordinaires, Dissertationes Math. 296 (1990), 1-79.
  • [13] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, Boston, London 1997.
  • [14] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore 1989.
  • [15] X. Liu, Nonlinear boundary value problems for first order impulsive differential equations, Appl. Anal. 36 (1990), 119-130.
  • [16] E. Liz and J.J. Nieto, Positive solutions of linear impulsive differential equations, Commun. Appl. Anal. 2 (4) (1998), 565-571.
  • [17] E. Liz, Problemas de frontera para nuevos tipos de ecuaciones diferenciales, Ph.D Thesis, Univ. Vigo (Spain) 1994 (in Spanish).
  • [18] M. Martelli, A Rothe's type theorem for non compact acyclic-valued maps, Boll. Un. Mat. Ital. 4 (3) (1975), 70-76.
  • [19] C. Pierson-Gorez, Problèmes aux Limites Pour des Equations Différentielles avec Impulsions, Ph.D. Thesis, Univ. Louvain-la-Neuve, Belgium 1993 (in French).
  • [20] A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore 1995.
  • [21] D. Yujun and Z. Erxin, An application of coincidence degree continuation theorem in existence of solutions of impulsive differential equations, J. Math. Anal. Appl. 197 (1996), 875-889.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1022
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