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Abstrakty
We propose a class of delay difference equation with piecewise constant nonlinearity. The convergence of solutions and the existence of globally asymptotically stable periodic solutions are investigated for such a class of difference equation.
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Czasopismo
Rocznik
Tom
Strony
121--128
Opis fizyczny
Bibliogr. 15 poz.
Bibliografia
- [1] 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.
- [2] 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(1988), 327-338.
- [3] COOKE K.L., WIENER J., A survey of differential equation with piecewise continuous argument, in Lecture Notes in Mathematics, Vol. 1475, 1-15, Springer-Verlag, Berlin 1991.
- [4] COOKE K.L., WIENER J., Retarded differential equations with piecewise constant delays, J. Math. Anal Appl, 99(1984), 265-297.
- [5] ELAYDI S., ZHANG S., Stability and periodicity of difference equations with finite delay, Funkcial Ekvac., 37(1994), 401-403.
- [6] GYÓRI I., LADAS G., Oscillation theory of delay differential equations with applications, Clarendon, Oxford 1991.
- [7] KURUKIS S.A., The asymptotic stability of xn+\ - axn + bxn-k = 0, J. Math. Anal. Appl., 188(1994), 719-731.
- [8] Kocic V.L., L ADAS G., Global attractivity in nonlinear delay difference equations, Proc. Amer. Math. Soc., 115(1992), 1083-1088.
- [9] LEVIN S.A., MAY R.M., A note on difference-delay equations, Theoret. Population Biol, 9(1976), 178-187.
- [10] SHAH S.M., WIENER J., Advanced differential equations with piecewise constant argument deviations, Inter. J. Math. Anal. Sci., 6(1983), 671-703.
- [11] SHEN J.H., STAVROULAKIS I.P., Oscillatory and nonoscillatory delay equations with piecewise constant argument, J. Math. Anal. Appl, 248(2000), 385-401.
- [12] WIENER J., SHAH S.M., Functional-differential equation with piecewise constant argument, Indian J. Math., 29(1987), 131-158.
- [13] WANG Y., YAN J., Necessary and sufficient condition for the global attractivity of the trivial solution of a delay equation with continuous and piecewise constant arguments, Appl. Math. Lett., 10(1997), 91-96.
- [14] Yu J.S., CHENG S.S., A stability criterion for a neutral difference equation with delay, Appl. Math. Lett., 7(1994), 75-80.
- [15] Yu J.S., CHANG E.G., WANG Z.C., Oscillation of delay difference equations, Appl. Anal., 53(1994), 117-124.
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Bibliografia
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bwmeta1.element.baztech-article-BPP1-0069-0087