An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces
Benchohra, Mouffak ; Boucherif, Abdelkader
Archivum Mathematicum, Tome 036 (2000), p. 159-169 / Harvested from Czech Digital Mathematics Library

In this paper, a nonlinear alternative for multivalued maps is used to investigate the existence of solutions of first order impulsive initial value problem for differential inclusions in Banach spaces.

Publié le : 2000-01-01
Classification:  34A37,  34A60,  34G25
@article{107728,
     author = {Mouffak Benchohra and Abdelkader Boucherif},
     title = {An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {159-169},
     zbl = {1054.34099},
     mrnumber = {1785033},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107728}
}
Benchohra, Mouffak; Boucherif, Abdelkader. An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces. Archivum Mathematicum, Tome 036 (2000) pp. 159-169. http://gdmltest.u-ga.fr/item/107728/

Aubin J. P.; Cellina A. Differential Inclusions, Springer-Verlag, Berlin-Heidelberg, 1984. (1984) | MR 0755330 | Zbl 0538.34007

Bainov D. D.; Simeonov P. S. Systems with Impulse Effect, Ellis Horwood Ltd., Chichister, 1989. (1989) | MR 1010418 | Zbl 0684.34056

Benchohra M. Existence of solutions for differential inclusions in Banach space, Commun. Appl. Anal. 4 (1) (2000), 71–77. | MR 1855983 | Zbl 1089.34540

Benchohra M.; Boucherif A. On first order initial value problems for impulsive differential inclusions in Banach Spaces, Dynam. Syst. Appl. 8 (1) (1999), 119–126. (1999) | MR 1669010 | Zbl 0929.34017

Deimling K. Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992. (1992) | MR 1189795 | Zbl 0820.34009

Erbe L.; Krawcewicz W. Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rockey Mountain J. Math. 22 (1992), 519–539. (1992) | MR 1180717 | Zbl 0784.34012

Frigon M.; O’Regan D. Existence results for first order impulsive differential equations, J. Math. Anal. Appl. 193 (1995), 96–113. (193 ) | MR 1338502

Frigon M.; O’Regan D., Boundary value problems for second order impulsive differential equations using set-valued maps, Rapport DMS-357, University of Montreal, 1993. (1993)

Frigon M. Application de la théorie de la transversalité topologique à des problèmes non linéaires pour des équations différentielles ordinaires, Dissertationes Math. 296 (1990), 1–79. (1990) | MR 1075674 | Zbl 0728.34017

Lakshmikantham V.; Bainov D. D.; Simeonov P. S. Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. (1989) | MR 1082551 | Zbl 0719.34002

Lasota A.; Opial Z. An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786. (1965) | MR 0196178 | Zbl 0151.10703

Liu X. Nonlinear boundary value problems for first order impulsive differential equations, Appl. Anal. 36 (1990), 119–130. (1990) | MR 1040882

Liz E. Boundary Value Problems for New Types of Differential Equations, Ph.D. Thesis, Univ. Santiago de Compostela, 1994 (in Spanish). (1994)

Liz E.; Nieto J. J. Positive solutions of linear impulsive differential equations, Commun. Appl. Anal. 2 (4) (1998), 565–571. (1998) | MR 1637016 | Zbl 0903.34017

O’Regan D. Fixed point theory for the sum of two operators, Appl. Math. Lett. 9 (1) (1996), 1–8. (1996) | Zbl 0858.34049

Pierson-Gorez C. Problèmes aux Limites Pour des Equations Différentielles avec Impulsions, Ph.D. Thesis, Univ. Louvain-la-Neuve, 1993 (in French). (1993)

Samoilenko A. M.; Perestyuk N. A. Impulsive Differential Equations, World Scientific, Singapore, 1995. (1995) | MR 1355787 | Zbl 0837.34003

Silva G. N.; Vinter R. B. Measure driven differential inclusions, J. Math. Anal. Appl. 202 (1996), 727–746. (1996) | MR 1408351 | Zbl 0877.49004

Stewart D. E. Existence of solutions to rigid body dynamics and the Painleve paradoxes, C. R. Acad. Sci. Paris Ser. I Math. 325 (1997), 689–693. (1997) | MR 1473847 | Zbl 0894.70006

Yosida K. Functional Analysis, $6^{\text{th}}$ edn. Springer-Verlag, Berlin, 1980. (1980) | MR 0617913 | Zbl 0435.46002

Yujun D.; Erxin Z. An application of coincidence degree continuation theorem in existence of solutions of impulsive differential equations, J. Math. Anal. Appl. 197 (1996), 875–889. (197 ) | MR 1373086