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Title: Oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales (English)
Author: Benchohra, Mouffak
Author: Hamani, Samira
Author: Henderson, Johnny
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 43
Issue: 4
Year: 2007
Pages: 237-250
Summary lang: English
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Category: math
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Summary: In this paper we discuss the existence of oscillatory and nonoscillatory solutions for first order impulsive dynamic inclusions on time scales. We shall rely of the nonlinear alternative of Leray-Schauder type combined with lower and upper solutions method. (English)
Keyword: impulsive dynamic inclusion
Keyword: oscillatory
Keyword: convex valued multivalued
Keyword: nonoscillatory
Keyword: delta derivative
Keyword: fixed point
Keyword: time scale
Keyword: upper and lower solutions
MSC: 34A37
MSC: 34A60
MSC: 34C10
MSC: 39A10
MSC: 39A12
idZBL: Zbl 1164.34003
idMR: MR2378524
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Date available: 2008-06-06T22:51:26Z
Last updated: 2012-05-10
Stable URL: http://hdl.handle.net/10338.dmlcz/108068
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Reference: [1] Agarwal R. P., Benchohra M., O’Regan D., Ouahab A.: Second order impulsive dynamic equations on time scales.Funct. Differ. Equ. 11 (2004), 223–234. MR 2095486
Reference: [2] Agarwal R. P., Bohner M., Saker S. H.: Oscillation of second order delay dynamic equations.Canad. Appl. Math. Quart. 13 (1), (2005), 1-17. Zbl 1126.39003, MR 2236199
Reference: [3] Agarwal R. P., O’Regan D., Wong P. J. Y.: Positive Solutions of Differential, Difference and Integral Equations.Kluwer Academic Publishers, Dordrecht, 1999. Zbl 1157.34301, MR 1680024
Reference: [4] Agarwal R. P., Grace S. R., O’Regan D.: Oscillation Theory for Second Order Dynamic Equations.Taylor Francis, Ltd., London, 2003. Zbl 1043.34032, MR 1965832
Reference: [5] Aulbach B., Hilger S.: Linear dynamic processes with inhomogeneous time scale. Nonlinear dynamics and quantum dynamical systems.Akademie-Verlag, Berlin, Math. Res. 59 (1990), 9–20. MR 1068548
Reference: [6] Bainov D. D., Simeonov P. S.: Systems with Impulse Effect.Ellis Horwood Ltd., Chichister, 1989. Zbl 0684.34056, MR 1010418
Reference: [7] Bainov D. D., Simeonov P. S.: Oscillation Theory of Impulsive Differential Equations.International Publications Orlando, Florida, 1998. Zbl 0949.34002, MR 1459713
Reference: [8] Benchohra M., Boucherif A.: An existence results for first order initial value problems for impulsive differential inclusions in Banach spaces.Arch. Math. (Brno) 36 (2000), 159–169. MR 1785033
Reference: [9] Benchohra M., Hamani S., Henderson J.: Oscillation and nonoscillation for impulsive dynamic equations on certain time scales.Adv. Differential Equations 2006 (2006), Article ID 60860, 12 pages. Zbl 1139.39008, MR 2255161
Reference: [10] Benchohra M., Henderson J., Ntouyas S. K.: Impulsive Diferential Equations and Inclusions.Hindawi Publishing Corporation, Vol. 2, New York, 2006.
Reference: [11] Benchohra M., Henderson J., Ntouyas S. K., Ouahab A.: On first order impulsive dynamic equations on time scales.J. Differ. Equations Appl. 10 (2004), 541–548. Zbl 1054.39012, MR 2060411
Reference: [12] Benchohra M., Ntouyas S. K., Ouahab A.: Existence results for second order boundary value problem of impulsive dynamic equations on time scales.J. Math. Anal. Appl. 296 (2004), 65–73. Zbl 1060.34017, MR 2070493
Reference: [13] Bohner E. A., Bohner M., Saker S. H.: Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations.Electronic Trans. Numerical Anal. 27 (2007), 1–12. Zbl 1177.34047, MR 2346144
Reference: [14] Bohner M., Peterson A.: Dynamic Equations on Time Scales: An Introduction with Applications.Birkhäuser, New York, 2001. Zbl 0978.39001, MR 1843232
Reference: [15] Bohner M., Peterson A., editors: Advances in Dynamic Equations on Time Scales.Birkhäuser, Boston, 2003. MR 1962542
Reference: [16] Bohner M., Saker S. H.: Oscillation of second order nonlinear dynamic equations on time scales.Rocky Mountain J. Math. 34 (2004), 1239–1254. Zbl 1075.34028, MR 2095254
Reference: [17] Bohner M., Tisdell C.: Second order dynamic inclusion.J. Nonlinear Math. Phys. 12 (2005), 36–45. MR 2217094
Reference: [18] Deimling K.: Multivalued Differential Equations.Walter De Gruyter, Berlin-New York, 1992. Zbl 0820.34009, MR 1189795
Reference: [19] Erbe L.: Oscillation criteria for second order linear equations on a time scale.Canad. Appl. Math. Quart. 9 (2001), 1–31. Zbl 1050.39024, MR 1975729
Reference: [20] Erbe L., Peterson A., Saker S. H.: Oscillation criteria for second order nonlinear dynamic equations on a time scale.J. London Math. Soc. 67 (2003), 701–714. MR 1967701
Reference: [21] 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 (14), (2000), 1–12. Zbl 0971.34022, MR 1798664
Reference: [22] Graef J. R., Karsai J.: Oscillation and nonoscillation in nonlinear implusive system with increasing energy.in Proceeding of the Third International Conference on Dynamical systems and Differential Equations, Discrete Contin. Dynam. Systems 7 (2000), 161–173. MR 1798664
Reference: [23] Granas A., Dugundji J.: Fixed Point Theory.Springer-Verlag, New York, 2003. Zbl 1025.47002, MR 1987179
Reference: [24] Henderson J.: Nontrivial solutions to a nonlinear boundary value problem on a times scale.Comm. Appl. Nonlinear Anal. 11 (2004), 65–71. MR 2028694
Reference: [25] Henderson J.: Double solutions of impulsive dynamic boundary value problems on a time scale.J. Differ. Equations Appl. 8 (2002), 345–356. Zbl 1003.39019, MR 1897856
Reference: [26] Henderson J., Tisdell C.: Topological transversality and boundary value problems on time scales.J. Math. Anal. Appl. 289 (2004), 110–125. Zbl 1047.34014, MR 2020531
Reference: [27] Hu, Sh., Papageorgiou N.: Handbook of Multivalued Analysis, Volume I: Theory.Kluwer, Dordrecht, 1997. Zbl 0887.47001, MR 1485775
Reference: [28] Lakshmikantham V., Bainov D. D., Simeonov P. S.: Theory of Impulsive Differential Equations.World Scientific, Singapore, 1989. Zbl 0719.34002, MR 1082551
Reference: [29] Lakshmikantham V., Sivasundaram S., Kaymakcalan B.: Dynamic Systems on Measure Chains.Kluwer Academic Publishers, Dordrecht, 1996. Zbl 0869.34039, MR 1419803
Reference: [30] Saker S. H.: Oscillation of nonlinear dynamic equations on time scales.Appl. Math. Comp. 148 (2004), 81–91. Zbl 1045.39012, MR 2014626
Reference: [31] Samoilenko A. M., Perestyuk N. A.: Impulsive Differential Equations.World Scientific, Singapore, 1995. Zbl 0837.34003, MR 1355787
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