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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1022,
author = {Mouffak Benchohra and Abdelkader Boucherif and Juan J. Nieto},
title = {On initial value problems for a class of first order impulsive differential inclusions},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {21},
year = {2001},
pages = {159-171},
zbl = {1005.34007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1022}
}
Mouffak Benchohra; Abdelkader Boucherif; Juan J. Nieto. On initial value problems for a class of first order impulsive differential inclusions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 21 (2001) pp. 159-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1022/
[000] [1] J.P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Boston 1990.
[001] [2] J.M. Ayerbe, T. Dominguez and G. Lopez-Acebo, Measure of Noncompactness in Metric Fixed Point Theory, Birkhäuser, Basel 1997. | Zbl 0885.47021
[002] [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York 1980. | Zbl 0441.47056
[003] [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. | Zbl 0929.34017
[004] [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. | Zbl 0988.34005
[005] [6] K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992.
[006] [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. | Zbl 0784.34012
[007] [8] D. Franco, Problemas de frontera para ecuaciones diferenciales con impulsos, Ph.D Thesis, Univ. Santiago de Compostela (Spain), 2000 (in Spanish).
[008] [9] M. Frigon and D. O'Regan, Existence results for first order impulsive differential equations, J. Math. Anal. Appl. 193, (1995), 96-113. | Zbl 0853.34011
[009] [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.
[010] [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. | Zbl 0930.34016
[011] [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.
[012] [13] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, Boston, London 1997.
[013] [14] V. Lakshmikantham, D.D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore 1989. | Zbl 0719.34002
[014] [15] X. Liu, Nonlinear boundary value problems for first order impulsive differential equations, Appl. Anal. 36 (1990), 119-130. | Zbl 0671.34018
[015] [16] E. Liz and J.J. Nieto, Positive solutions of linear impulsive differential equations, Commun. Appl. Anal. 2 (4) (1998), 565-571. | Zbl 0903.34017
[016] [17] E. Liz, Problemas de frontera para nuevos tipos de ecuaciones diferenciales, Ph.D Thesis, Univ. Vigo (Spain) 1994 (in Spanish).
[017] [18] M. Martelli, A Rothe's type theorem for non compact acyclic-valued maps, Boll. Un. Mat. Ital. 4 (3) (1975), 70-76. | Zbl 0314.47035
[018] [19] C. Pierson-Gorez, Problèmes aux Limites Pour des Equations Différentielles avec Impulsions, Ph.D. Thesis, Univ. Louvain-la-Neuve, Belgium 1993 (in French). | Zbl 0868.34007
[019] [20] A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore 1995.
[020] [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. | Zbl 0853.34010