×

New results on oscillation for delay differential equations with piecewise constant argument. (English) Zbl 1065.34061

This paper deals with the oscillatory behavior of solutions of first-order delay differential equations with oscillating coefficients and piecewise constant arguments. Examples are included to illustrate the importance of the results. Also see J. H. Shen and I. P. Stavroulakis [J. Math. Anal. Appl. 248, 385–401 (2000; Zbl 0966.34063)] and the authors [Tamkang J. Math. 32, 293–304 (2001; Zbl 1004.34056)].

MSC:

34K11 Oscillation theory of functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cooke, K. L.; Wiener, J., Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl., 99, 265-297 (1984) · Zbl 0557.34059
[2] Cooke, K. L.; Wiener, J., A survey of differential equations with piecewise constant argument, (Lecture Notes in Mathematics, Vol. 1475 (1991), Springer-Verlag: Springer-Verlag Berlin), 1-15 · Zbl 0737.34045
[3] Shah, S. M.; Wiener, J., Advanced differential equations with piece constant argumetn deviations, Inter. J. Math. and Math-Sci., 6, 671-703 (1983) · Zbl 0534.34067
[4] Aftabizadeh, A. R.; Wiener, J., Oscillatory properties of first order linear functional differential equations, Appl. Anal., 22, 165-187 (1985) · Zbl 0553.34045
[5] Aftabizadeh, A. R.; Wiener, J., Oscillatory and periodic solutions for systems of two first order linear differential equations with piecewise constant argument, Appl. Anal., 26, 327-338 (1988) · Zbl 0634.34051
[6] Aftabizadeh, A. R.; Wiener, J.; Xu, J. M., Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, (Proc. Amer. Math. Soc., 99 (1987)), 673-679 · Zbl 0631.34078
[7] Agwo, H. A., Necessary and sufficient conditions for the oscillation of delay differential equations with a piecewise constant argument, Internat. Math. and Math. Sci., 21, 493-498 (1998) · Zbl 0904.34052
[8] Cooke, K. L.; Wiener, J., An equation alternately of retarded and advanced type, (Proc. Amer. Math. Soc., 99 (1987)), 726-732 · Zbl 0628.34074
[9] Papaschinopoulos, G., Exponential dichotomy, topological equivalence and structural stability for differential equations with piecewise constant argument, Anal., 14, 239-247 (1994) · Zbl 0829.34055
[10] Shen, J.; Stavroulakis, I. P., Oscillatory and nonoscillatory delay differential equations with piecewise constant argument, J. Math. Anal. Appl., 248, 385-401 (2000) · Zbl 0966.34063
[11] Luo, Z.; Shen, J., Oscillation criteria for differential equations with piecewise constant argument, Tamkang J. Math., 32, 4, 293-304 (2001) · Zbl 1004.34056
[12] Yuan, R.; Hong, J. L., The existence of almost periodic solutions for a class of differential equations with piecewise constant arguments, Nonlinear Analysis, 28, 1439-1450 (1997) · Zbl 0869.34038
[13] Huang, Y. K., Oscillation and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument, J. Math. Anal. Appl., 149, 70-85 (1990) · Zbl 0704.34078
[14] Wiener, J.; Cooke, K. L., Oscillations in systems of differential equations with piecewise constant argument, J. Math. Anal. Appl., 137, 221-239 (1989) · Zbl 0728.34077
[15] Gopalsamy, K.; Kulenovic, M. R.S.; Ladas, G., On a logistic equations with piecewise constant arguments, Differential Integral Equations, 1, 305-314 (1988) · Zbl 0639.34070
[16] Gyori, I.; Ladas, G., Oscillation Theory of Delay Differential Equations with Applications, ((1991), Clarendon Press: Clarendon Press Oxford) · Zbl 0780.34048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.