# Article

Full entry | PDF   (0.3 MB)
Keywords:
neutral difference equations; oscillation; nonoscillation; asymptotic behaviour
Summary:
Necessary and sufficient conditions are obtained for every solution of $\Delta (y_{n}+p_{n}y_{n-m})\pm q_{n}G(y_{n-k})=f_{n}$ to oscillate or tend to zero as $n\rightarrow \infty$, where $p_{n}$, $q_{n}$ and $f_{n}$ are sequences of real numbers such that $q_{n}\ge 0$. Different ranges for $p_{n}$ are considered.
References:
[1] S. S.  Cheng and Y. Z.  Lin: Complete characterization of an oscillatory neutral difference equation. J. Math. Anal. Appl. 221 (1998), 73–91. DOI 10.1006/jmaa.1997.5341 | MR 1619135
[2] D. A.  Georgiou, E. A.  Grove and G.  Ladas: Oscillations of neutral difference equations. Appl. Anal. 33 (1989), 243–251. DOI 10.1080/00036818908839876 | MR 1030111
[3] D. A.  Georgiou, E. A.  Grove and G.  Ladas: Oscillation of neutral difference equations with variable coefficient. In: Differencial Equations: Stability and Control, Marcel Dekker, 1990, pp. 165–178. MR 1096752
[4] I. Gyori and G. Ladas: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991. MR 1168471
[5] B. S.  Lalli, B. G.  Zhang and J. Z.  Li: On the oscillation of solutions and existence of positive solutions of neutral difference equations. J.  Math. Anal. Appl. 158 (1991), 213–233. DOI 10.1016/0022-247X(91)90278-8 | MR 1113411
[6] B. S. Lalli and B. G. Zhang: On existence of positive solutions and bounded oscillations for neutral difference equations. J.  Math. Anal. Appl. 166 (1992), 272–287. DOI 10.1016/0022-247X(92)90342-B | MR 1159653
[7] N. Parhi and A. K. Tripathy: Oscillation criteria for forced non-linear neutral delay difference equations of first order. Differential Equations Dynam. Systems 8 (2000), 81–97. MR 1858770
[8] N. Parhi and R. N. Rath: Oscillation criteria for forced first order neutral differential equations with variable coefficients. J.  Math. Anal. Appl. 256 (2001), 525–541. DOI 10.1006/jmaa.2000.7315 | MR 1821755
[9] E.  Thandapani et al: Asymptotic behaviour and oscillation of solutions of neutral delay-difference equations of arbitary order. Math. Slovaca 47 (1997), 539–551. MR 1635228
[10] B. G.  Zhang and S. S.  Cheng: Oscillation criteria and comparision theorems for delay-difference equations. Fasc. Math. 25 (1995), 13–32. MR 1339622

Partner of