Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument

Acta Applicandae Mathematicae

Volumn 110, Issue 1, 2010, Pages 499-510

  Karakoc, Fatma ^a   Bereketoglu, Huseyin ^a   Seyhan, Gizem ^a  

^a ANKARA UNIVERSITY   (Turkey)

Author keywords

Difference equation; Differential equation with piecewise constant argument; Impulsive delay differential equation; Oscillatory solution; Periodic solution

Indexed keywords

IMPULSIVE DELAY DIFFERENTIAL EQUATION; OSCILLATORY SOLUTIONS; PERIODIC SOLUTION; PIECEWISE CONSTANT ARGUMENT;

PROBLEM SOLVING; SECURITY OF DATA;

DIFFERENCE EQUATIONS;

EID: 77952097381     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-009-9458-9     Document Type: Article

References (22)

1. A.R. Aftabizadeh J. Wiener J. Ming Xu 1987 Oscillatory and periodic solutions of delay differential equations with piecewise constant argument Proc. Am. Math. Soc. 99 673 679 0631.34078 10.2307/2046474
2. H. Bereketoǧlu F. Karakoç 2008 Asymptotic constancy for impulsive delay differential equations Dyn. Syst. Appl. 17 71 84 1159.34052
3. Bereketoǧlu, H., Pituk, M.: Asymptotic constancy for nonhomogeneous linear differential equations with unbounded delays. Discrete Continuous Dyn. Syst. Suppl., 100-107 (2003)
4. Busenberg, S., Cooke, K.L.: Models of vertically transmitted diseases with sequential-continuous dynamics. In: Lakshmikantham, V. (ed.) Nonlinear Phenomena in Mathematical Sciences, pp. 179-187. Academic Press, New York (1982)
5. K.L. Cooke J. Wiener 1984 Retarded differential equations with piecewise constant delays J. Math. Anal. Appl. 99 265 297 0557.34059 10.1016/0022-247X(84) 90248-8 732717
6. L. Dai M.C. Singh 1994 On oscillatory motion of spring-mass systems subject to piecewise constant forces J. Sound Vib. 173 217 233 1078.70506 10.1006/jsvi.1994.1227
7. L. Dai M.C. Singh 1997 An analytical and numerical method for solving linear and nonlinear vibration problems Int. J. Solids Struct. 34 2709 2731 0942.74663 10.1016/S0020-7683(96)00169-2 1454992 (Pubitemid 127419873)
8. L. Dai M.C. Singh 1998 Periodic, quasiperiodic and chaotic behavior of a driven Froude pendulum Int. J. Non-Linear Mech. 33 947 965 05137826 10.1016/S0020-7462(97)00054-1 1623494 (Pubitemid 128416450)
9. -(t)=β(t)[y(t)-y(t-τ(t))] J. Math. Anal. Appl. 217 200 215 0892.34067 10.1006/jmaa.1997.5709 1492085 (Pubitemid 128341121)
10. J. Diblik 1998 Behaviour of solutions of linear differential equations with delay Arch. Math. (Brno) 34 31 47 0914.34065 1629652
11. K. Gopalsamy B.G. Zhang 1989 On delay differential equations with impulses J. Math. Anal. Appl. 139 110 122 0687.34065 10.1016/0022-247X(89)90232- 1 991929
12. I. Gyori 1991 On approximation of the solutions of delay differential equations by using piecewise constant arguments Int. J. Math. Math. Sci. 14 111 126 10.1155/S016117129100011X
13. Gyori, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford (1991)
14. Karakoc, F., Bereketoglu, H.: Some results for linear impulsive delay differential equations. Dyn. Cont. Discrete Impulsive Syst. (to appear)
15. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
16. J. Li J. Shen 2002 Periodic boundary value problems of impulsive differential equations with piecewise constant argument J. Nat. Sci. Hunan Norm. Univ. 25 5 9 1939990 (Pubitemid 36430017)
17. Murad, N.M., Celeste, A.: Linear and nonlinear characterisation of loading systems under piecewise discontinuous disturbances voltage: analytical and numerical approaches. In: Proceedings of International Conference on Power Electronic Systems and Applications, pp. 291-297 (2004) (Pubitemid 43346051)
18. J.H. Shen I.P. Stavroulakis 2000 Oscillatory and nonoscillatory delay equations with piecewise constant argument J. Math. Anal. Appl. 248 385 401 0966.34063 10.1006/jmaa.2000.6908 1775858
19. Wiener, J.: Generalized Solutions of Functional Differential Equations. World Scientific, Singapore (1994)
20. J. Wiener V. Lakshmikantham 2000 Differential equations with piecewise constant argument and impulsive equations Nonlinear Stud. 7 60 69 0997.34076 1856579
21. Y. Zhang A. Zhao J. Yan 1997 Oscillation criteria for impulsive delay differential equations J. Math. Anal. Appl. 205 461 470 0870.34071 10.1006/jmaa.1997.5211 1428360 (Pubitemid 127170290)
22. A. Zhao J. Yan 1997 Necessary and sufficient conditions for oscillations of delay equations with impulses Appl. Math. Lett. 10 23 29 0889.34060 10.1016/S0893-9659(96)00105-X 1429470 (Pubitemid 127413331)