| Title:
|
On oscillatory nonlinear fourth-order difference equations with delays (English) |
| Author:
|
Tripathy, Arun K. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
25-40 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form \begin {equation*} \Delta ^{2}(r(n)\Delta ^{2}(y(n)+p(n)y(n-m)))+ q(n)G(y(n-k))=0 \end {equation*} is studied under the assumption \begin {equation*} \sum _{n=0}^{\infty }\frac {n}{r(n)}< \infty . \end {equation*} New oscillation criteria have been established which generalize some of the existing results in the literature. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
nonlinear |
| Keyword:
|
delay |
| Keyword:
|
neutral functional difference equation |
| MSC:
|
39A10 |
| MSC:
|
39A12 |
| idZBL:
|
Zbl 06861590 |
| idMR:
|
MR3778048 |
| DOI:
|
10.21136/MB.2017.0018-16 |
| . |
| Date available:
|
2018-03-19T10:33:27Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147140 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications.Birkhäuser, Basel (2001). Zbl 0978.39001, MR 1843232, 10.1007/978-1-4612-0201-1 |
| Reference:
|
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| Reference:
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[5] Graef, J. R., Miciano, A., Spikes, P., Sundaram, P., Thandapani, E.: Oscillatory and asymptotic behaviour of solutions of nonlinear neutral-type difference equations.J. Aust. Math. Soc., Ser. B 38 (1996), 163-171. Zbl 0890.39018, MR 1414357, 10.1017/S0334270000000552 |
| Reference:
|
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| Reference:
|
[7] Gyori, I., Ladas, G.: Oscillation Theory for Delay Differential Equations with Applications.Oxford Mathematical Monographs. Clarendon Press, Oxford (1991). Zbl 0780.34048, MR 1168471 |
| Reference:
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[8] Migda, M.: Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations.Opusc. Math. 26 (2006), 507-514. Zbl 1131.39008, MR 2280277 |
| Reference:
|
[9] Migda, M., Migda, J.: Oscillatory and asymptotic properties of solutions of even order neutral difference equations.J. Difference Equ. Appl. 15 (2009), 1077-1084. Zbl 1194.39009, MR 2569136, 10.1080/10236190903032708 |
| Reference:
|
[10] Parhi, N., Tripathy, A. K.: Oscillation of a class of nonlinear neutral difference equations of higher order.J. Math. Anal. Appl. 284 (2003), 756-774. Zbl 1037.39002, MR 1998666, 10.1016/S0022-247X(03)00298-1 |
| Reference:
|
[11] Thandapani, E., Arockiasamy, I. M.: Oscillatory and asymptotic behaviour of fourth order nonlinear neutral delay difference equations.Indian J. Pure Appl. Math. 32 (2001), 109-123. Zbl 1004.39005, MR 1819234 |
| Reference:
|
[12] Thandapani, E., Sundaram, P., Graef, J. R., Miciano, A., Spikes, P.: Classification of non-oscillatory solutions of higher order neutral type difference equations.Arch. Math. (Brno) 31 (1995), 263-277. Zbl 0855.39014, MR 1390585 |
| Reference:
|
[13] Tripathy, A. K.: Oscillation of fourth-order nonlinear neutral difference equations II.Math. Slovaca 58 (2008), 581-604. Zbl 1199.39018, MR 2434679 |
| Reference:
|
[14] Tripathy, A. K.: New oscillation criteria for fourth order nonlinear neutral difference equations.Adv. Dyn. Syst. Appl 8 (2013), 387-399. MR 3162156 |
| . |
