Title:
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Oscillatory and nonoscillatory solutions for first order impulsive differential inclusions (English) |
Author:
|
Benchohra, Mouffak |
Author:
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Ouahab, Abdelghani |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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46 |
Issue:
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3 |
Year:
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2005 |
Pages:
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541-553 |
. |
Category:
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math |
. |
Summary:
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In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method. (English) |
Keyword:
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impulsive differential inclusions |
Keyword:
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lower and upper solution |
Keyword:
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existence |
Keyword:
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nonoscillatory |
Keyword:
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oscillatory |
Keyword:
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fixed point |
MSC:
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34A37 |
MSC:
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34A60 |
MSC:
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34C10 |
idZBL:
|
Zbl 1121.34011 |
idMR:
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MR2174531 |
. |
Date available:
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2009-05-05T16:53:10Z |
Last updated:
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2012-04-30 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/119547 |
. |
Reference:
|
[1] Agarwal R.P., Grace S.R., O'Regan D.: Oscillation Theory for Second Order Dynamic Equations.Series in Mathematical Analysis and Applications, Taylor & Francis, Ltd., London, 2003. Zbl 1043.34032, MR 1965832 |
Reference:
|
[2] Agarwal R.P., Grace S.R., O'Regan D.: On nonoscillatory solutions of differential inclusions.Proc. Amer. Math. Soc. 131 1 (2003), 129-140. Zbl 1009.47052, MR 1929032 |
Reference:
|
[3] Agarwal R.P., Grace S.R., O'Regan D.: Oscillation criteria for sublinear and superlinear second order differential inclusions.Mem. Differential Equations Math. Phys. 28 (2003), 1-12. Zbl 1059.34008, MR 1986714 |
Reference:
|
[4] Bainov D.D., Simeonov P.S.: Systems with Impulse Effect.Ellis Horwood Ltd., Chichister, 1989. Zbl 0714.34083, MR 1010418 |
Reference:
|
[5] Bainov D., Simeonov P.: Oscillations Theory of Impulsive Differential Equations.International Publications Orlando, Florida, 1998. MR 1459713 |
Reference:
|
[6] Benchohra M., Boucherif A.: Initial value problems for impulsive differential inclusions of first order.Differential Equations Dynam. Systems 8 (2000), 51-66. Zbl 0988.34005, MR 1858768 |
Reference:
|
[7] Benchohra M., Henderson J., Ntouyas S.K.: On first order impulsive differential inclusions with periodic boundary conditions.Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 9 3 (2002), 417-427. Zbl 1017.34008, MR 1897802 |
Reference:
|
[8] Benchohra M., Ntouyas S.K.: The lower and upper solutions method for first order differential inclusions with nonlinear boundary conditions.J. Inequal. Pure Appl. Math. 3 (2002), 1 Article 14, 8 pp. Zbl 1003.34013, MR 1888929 |
Reference:
|
[9] Benchohra M., Henderson J., Ntouyas S.K., Ouahab A.: Upper and lower solutions method for first order impulsive differential inclusions with nonlinear boundary conditions.Comput. Math. Appl. 47 (2004), 1069-1078. Zbl 1068.34009, MR 2060337 |
Reference:
|
[10] Bohnenblust H.F., Karlin S.: On a theorem of Ville. Contributions to the theory of games.pp.155-160, Annals of Mathematics Studies, no. 24. Princeton University Press, Princeton, N.J., 1950. MR 0041415 |
Reference:
|
[11] Deimling K.: Multivalued Differential Equations.Walter De Gruyter, Berlin-New York, 1992. Zbl 0820.34009, MR 1189795 |
Reference:
|
[12] Erbe L.H., Kong Q.K., Zhang B.G.: Oscillation Theory for Functional Differential Equations.Marcel Dekker, New York, 1995. Zbl 0821.34067, MR 1309905 |
Reference:
|
[13] Graef J.R., Karsai J.: On the oscillation of impulsively damped halflinear oscillators.Proc. Sixth Colloquium Qual. Theory Differential Equations, Electron. J. Qual. Theory Differential Equations no. 14 (2000), 1-12. Zbl 0971.34022, MR 1798664 |
Reference:
|
[14] Graef J.R., Karsai J.: Oscillation and nonoscillation in nonlinear impulsive systems with increasing energy.in Proceeding of the Third International Conference on Dynamical systems and Differential Equations, Discrete Contin. Dynam. Syst. 7 (2000), 161-173. MR 1798664 |
Reference:
|
[15] Graef J.R., Karsai J., Yang B.: Nonoscillation results for nonlinear impulsive systems with nondecreasing energy.Dyn. Contin. Discrete Impuls. Systems, to appear. |
Reference:
|
[16] Gyori I., Ladas G.: Oscillation Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 |
Reference:
|
[17] Hu Sh., Papageorgiou N.: Handbook of Multivalued Analysis.Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997. Zbl 0943.47037, MR 1485775 |
Reference:
|
[18] Ladde G.S., Lakshmikantham V., Zhang B.G.: Oscillation Theory for Differential Equations with Deviating Arguments.Marcel Dekker, New York, 1987. MR 1017244 |
Reference:
|
[19] 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:
|
[20] Lakshmikantham V., Bainov D.D., Simeonov P.S.: Theory of Impulsive Differential Equations.World Scientific, Singapore, 1989. Zbl 0719.34002, MR 1082551 |
Reference:
|
[21] Samoilenko A.M., Perestyuk N.A.: Impulsive Differential Equations.World Scientific, Singapore, 1995. MR 1355787 |
Reference:
|
[22] Yong-shao C., Wei-zhen F.: Oscillation of second order nonlinear ODE with impulses.J. Math. Anal. Appl. 20 (1997), 150-169. MR 1449514 |
Reference:
|
[23] Zeidler E.: Nonlinear Functional Analysis and Applications, Fixed Point Theorems.Springer, New York, 1986. MR 0816732 |
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