| Title:
|
Oscillation of forced nonlinear neutral delay difference equations of first order (English) |
| Author:
|
Parhi, N. |
| Author:
|
Tripathy, A. K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
83-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
neutral difference equations |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
asymptotic behaviour |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
39A12 |
| idZBL:
|
Zbl 1016.39011 |
| idMR:
|
MR1962001 |
| . |
| Date available:
|
2009-09-24T10:59:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127783 |
| . |
| Reference:
|
[1] S. S. Cheng and Y. Z. Lin: Complete characterization of an oscillatory neutral difference equation.J. Math. Anal. Appl. 221 (1998), 73–91. MR 1619135, 10.1006/jmaa.1997.5341 |
| Reference:
|
[2] D. A. Georgiou, E. A. Grove and G. Ladas: Oscillations of neutral difference equations.Appl. Anal. 33 (1989), 243–251. MR 1030111, 10.1080/00036818908839876 |
| Reference:
|
[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 |
| Reference:
|
[4] I. Gyori and G. Ladas: Oscillation Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[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. MR 1113411, 10.1016/0022-247X(91)90278-8 |
| Reference:
|
[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. MR 1159653, 10.1016/0022-247X(92)90342-B |
| Reference:
|
[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 |
| Reference:
|
[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. MR 1821755, 10.1006/jmaa.2000.7315 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| . |
