Title:
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An existence result for first order initial value problems for impulsive differential inclusions in Banach spaces (English) |
Author:
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Benchohra, Mouffak |
Author:
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Boucherif, Abdelkader |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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36 |
Issue:
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3 |
Year:
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2000 |
Pages:
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159-169 |
Summary lang:
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English |
. |
Category:
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math |
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Summary:
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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. (English) |
Keyword:
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impulsive initial value problem |
Keyword:
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multivalued map |
Keyword:
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a priori bounds |
Keyword:
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existence |
Keyword:
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fixed point |
MSC:
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34A37 |
MSC:
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34A60 |
MSC:
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34G25 |
idZBL:
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Zbl 1054.34099 |
idMR:
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MR1785033 |
. |
Date available:
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2008-06-06T22:25:38Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/107728 |
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Reference:
|
[1] Aubin J. P., Cellina A.: Differential Inclusions.Springer-Verlag, Berlin-Heidelberg, 1984. Zbl 0538.34007, MR 0755330 |
Reference:
|
[2] Bainov D. D., Simeonov P. S.: Systems with Impulse Effect.Ellis Horwood Ltd., Chichister, 1989. Zbl 0684.34056, MR 1010418 |
Reference:
|
[3] Benchohra M.: Existence of solutions for differential inclusions in Banach space.Commun. Appl. Anal. 4 (1) (2000), 71–77. Zbl 1089.34540, MR 1855983 |
Reference:
|
[4] 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. Zbl 0929.34017, MR 1669010 |
Reference:
|
[5] Deimling K.: Multivalued Differential Equations.Walter De Gruyter, Berlin-New York, 1992. Zbl 0820.34009, MR 1189795 |
Reference:
|
[6] 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. Zbl 0784.34012, MR 1180717 |
Reference:
|
[7] Frigon M., O’Regan D.: Existence results for first order impulsive differential equations.J. Math. Anal. Appl. 193 (1995), 96–113. MR 1338502 |
Reference:
|
[8] 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. |
Reference:
|
[9] 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. Zbl 0728.34017, MR 1075674 |
Reference:
|
[10] Lakshmikantham V., Bainov D. D., Simeonov P. S.: Theory of Impulsive Differential Equations.World Scientific, Singapore, 1989. Zbl 0719.34002, MR 1082551 |
Reference:
|
[11] 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. Zbl 0151.10703, MR 0196178 |
Reference:
|
[12] Liu X.: Nonlinear boundary value problems for first order impulsive differential equations.Appl. Anal. 36 (1990), 119–130. MR 1040882 |
Reference:
|
[13] Liz E.: Boundary Value Problems for New Types of Differential Equations.Ph.D. Thesis, Univ. Santiago de Compostela, 1994 (in Spanish). |
Reference:
|
[14] Liz E., Nieto J. J.: Positive solutions of linear impulsive differential equations.Commun. Appl. Anal. 2 (4) (1998), 565–571. Zbl 0903.34017, MR 1637016 |
Reference:
|
[15] O’Regan D.: Fixed point theory for the sum of two operators.Appl. Math. Lett. 9 (1) (1996), 1–8. Zbl 0858.34049 |
Reference:
|
[16] Pierson-Gorez C.: Problèmes aux Limites Pour des Equations Différentielles avec Impulsions.Ph.D. Thesis, Univ. Louvain-la-Neuve, 1993 (in French). |
Reference:
|
[17] Samoilenko A. M., Perestyuk N. A.: Impulsive Differential Equations.World Scientific, Singapore, 1995. Zbl 0837.34003, MR 1355787 |
Reference:
|
[18] Silva G. N., Vinter R. B.: Measure driven differential inclusions.J. Math. Anal. Appl. 202 (1996), 727–746. Zbl 0877.49004, MR 1408351 |
Reference:
|
[19] 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. Zbl 0894.70006, MR 1473847 |
Reference:
|
[20] Yosida K.: Functional Analysis.$6^{\text{th}}$ edn. Springer-Verlag, Berlin, 1980. Zbl 0435.46002, MR 0617913 |
Reference:
|
[21] 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. MR 1373086 |
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