×

Asymptotic behaviour and oscillation of solutions of neutral delay difference equations of arbitrary order. (English) Zbl 0941.39006

Summary: The authors obtain results on the asymptotic properties of solutions of a higher order nonlinear neutral delay difference equation. Examples illustrating the results are included and some suggestions for further research are indicated.

MSC:

39A11 Stability of difference equations (MSC2000)
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] AGARWAL R. P.: Difference Equations and Inequalities. Marcel Dekker, New York, 1992. · Zbl 0925.39001
[2] BYKOV, YA. V.-ZHIVOGLYADOVA L. V.-SHEVTSOV E. I.: Sufficient conditions for solutions of nonlinear finite-difference equations to have the oscillatory property. Differentsiaľnye Uravneniya 9 (1973), 1523-1524.
[3] BYKOV, YA. V., ZHIVOGLYADOVA L. V.: Oscillatory properties of solutions of nonlinear finite-difference equations. Differentsiaľnye Uravneniya 9 (1973), 2080-2081.
[4] BYKOV, YA. V.-SHEVTSOV E. I.: Sufficient conditions for the oscillation of solutions of nonlinear finite-difference equations. Differentsiaľnye Uravneniya 9 (1973), 2241-2244.
[5] CHENG S. S.-YAN T. C.-LI H. J.: Oscillation criteria for second order difference equation. Funkcial. Ekvac. 34 (1991), 223-239. · Zbl 0773.39001
[6] CHUANXI Q.-LADAS G.: Oscillatory behavior of difference equations with positive and negative coefficients. Matematiche (Catania) 44 (1989), 293-310. · Zbl 0822.39001
[7] ERBE L. H.-ZHANG B. G.: Oscillation of discrete analogues of delay equations. Differential Integral Equations 2 (1989), 300-309. · Zbl 0723.39004
[8] ERBE L.-ZHANG B. G.: Oscillation of difference equations with delay. Differential Equations and Applications Vol. I (A. R. Aftabizadeh, Ohio U. Press, Athens, 1989, pp. 257-263. · Zbl 0722.39003
[9] GEORGIOU D. A.-GROVE E. A.-LADAS G.: Oscillations of neutral difference equations. Appl. Anal. 33 (1989), 243-253. · Zbl 0685.39003
[10] GEORGIOU D. A.-GROVE E. A.-LADAS G.: Oscillation of neutral difference equations with variable coefficients. ”Differential Equations, Stability and Control” (S. Elaydi, Lecture Notes in Pure and Appl. Math. 127, Dekker, New York, 1991, pp. 165-173.
[11] HE X.-Z.: Oscillatory and asymptotic behaviour of second order nonlinear difference equations. J. Math. Anal. Appl. 175 (1993), 482-498. · Zbl 0780.39001
[12] HOOKER J. W.-PATULA W. T.: A second-order nonlinear difference equation: oscillation and asymptotic behavior. J. Math. Anal. Appl. 91 (1983), 9-29. · Zbl 0508.39005
[13] JAROŠ J.-STAVROULAKIS I. P.: Necessary and sufficient conditions for oscillations of difference equations with several delays. · Zbl 0808.39004
[14] LADAS G.: Explicit conditions for the oscillation of difference equations. J. Math. Anal. Appl. 153 (1990), 276-287. · Zbl 0718.39002
[15] LADAS G.: Recent developments in the oscillation of delay difference equations. ”Differential Equations, Stability and Control” (S. Elaydi, Lecture Notes in Pure and Appl. Math. 127, Dekker, New York, 1991, pp. 321-332.
[16] LADAS G.-PHILOS, CH. G.-SFICAS Y. G.: Sharp conditions for the oscillation of delay difference equations. J. Appl. Math. Simm. 2 (1989), 101-111. · Zbl 0685.39004
[17] LAKSHMIKANTHAM V.-TRIGIANTE D.: Theory of Difference Equations: Numerical Methods and Applications. Math. Sci. Engrg. 181, Academic Press, New York, 1988. · Zbl 0683.39001
[18] LALLI B. S.-ZHANG B. G.: On existence of positive solutions and bounded oscillations for neutral difference equations. J. Math. Anal. Appl. 166 (1992), 272-287. · Zbl 0763.39002
[19] LALLI B. S.-ZHANG B. G.: Oscillation and comparison theorems for certain neutral difference equations. J. Austral. Math. Soc. · Zbl 0759.39002
[20] LALLI B. S.-ZHANG B. G.-LI J. Z.: On the oscillation of solutions and existence of positive solutions of neutral difference equations. J. Math. Anal. Appl. 158 (1991), 213-233. · Zbl 0732.39002
[21] PATULA W. T.: Growth and oscillation properties of second order linear difference equations. SIAM J. Math. Anal. 10 (1979), 55-61. · Zbl 0397.39001
[22] PATULA W. T.: Growth, oscillation and comparison theorems for second order linear difference equations. SIAM J. Math. Anal. 10 (1979), 1272-1279. · Zbl 0433.39005
[23] SZMANDA B.: Oscillation theorems for nonlinear second-order difference equations. J. Math. Anal. Appl. 79 (1981), 90-95. · Zbl 0455.39004
[24] THANDAPANI E.: Asymptotic and oscillatory behavior of solutions of a second order nonlinear neutral delay difference equation. Riv. Math. Univ. Parma (5) 1 (1992), 105-113. · Zbl 0787.39003
[25] THANDAPANI E.-SUNDARAM P.: On the asymptotic and oscillatory behavior of solutions of second order nonlinear neutral difference equations. · Zbl 0862.39007
[26] THANDAPANI E.-SUNDARAM P.: Asymptotic and oscillatory behavior of solutions of first order nonlinear neutral difference equations. · Zbl 0901.39004
[27] THANDAPANI E.-SUNDARAM P., GRAEF J. R., SPIKES P. W.: Asymptotic properties of solutions of nonlinear second order neutral delay difference equations. Dynam. Systems Appl. 4 (1995), 125-136. · Zbl 0820.39005
[28] THANDAPANI E.-SUNDARAM P., GYORI I.: Oscillations of second order non-linear neutral delay difference equations. · Zbl 1028.39005
[29] WANG Z., YU J.: Oscillation criteria for second order nonlinear difference equations. Funkcial. Ekvac. 34 (1991), 313-319. · Zbl 0742.39003
[30] ZAFER A., DAHIYA R. S.: Oscillations of a neutral difference equation. Appl. Math. Lett. 6 (1993), 71-74. · Zbl 0772.39001
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.