| Title:
|
Classification of nonoscillatory solutions of higher order neutral type difference equations (English) |
| Author:
|
Thandapani, E. |
| Author:
|
Sundaram, P. |
| Author:
|
Graef, John R. |
| Author:
|
Miciano, A. |
| Author:
|
Spikes, Paul W. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
263-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The authors consider the difference equation \[ \Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \delta q_{n} y_{\sigma (n + m - 1)} = 0 \qquad \mathrm {(\ast )}\] where $m \ge 2$, $\delta = \pm 1$, $k \in N_0 = \lbrace 0,1, 2, \dots \rbrace $, $\Delta y_{n} = y_{n + 1} - y_{n}$, $q_{n} > 0$, and $\lbrace \sigma (n)\rbrace $ is a sequence of integers with $\sigma (n) \le n$ and $\lim _{n \rightarrow \infty } \sigma (n) = \infty $. They obtain results on the classification of the set of nonoscillatory solutions of ($\ast $) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included. (English) |
| Keyword:
|
difference equations |
| Keyword:
|
nonlinear |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
nonoscillatory solutions |
| MSC:
|
39A10 |
| MSC:
|
39A12 |
| idZBL:
|
Zbl 0855.39014 |
| idMR:
|
MR1390585 |
| . |
| Date available:
|
2008-06-06T21:29:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107547 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
Georgiou, D. A., Grove, E. A. and Ladas, G.: Oscillation of neutral difference equations.Appl. Anal. 33 (1989), 243–253. MR 1030111 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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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. MR 1230602 |
| Reference:
|
Thandapani, E., Sundaram, P., Graef, J. R. and Spikes, P. W.: Asymptotic properties of solutions of nonlinear second order neutral delay difference equations.Dynamic Syst. Appl. 4 (1995), 125–136. MR 1312484 |
| Reference:
|
Thandapani, E., Sundaram, P., Graef, J. R. and Spikes, P. W.: Asymptotic behavior and oscillation of solutions of neutral delay difference equations of arbitrary order.(to appear). MR 1635228 |
| Reference:
|
Thandapani, E., Sundaram, P. and Györi, I.: On the behavior of solutions of first order nonlinear neutral difference equations.(to appear). |
| Reference:
|
Thandapani, E., Sundaram, P. and Györi, I.: Oscillations of second order nonlinear neutral delay difference equations.(to appear). MR 1867518 |
| Reference:
|
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| . |
