| Title:
|
Oscillation of a nonlinear difference equation with several delays (English) |
| Author:
|
Luo, X. N. |
| Author:
|
Zhou, Yong |
| Author:
|
Li, C. F. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
309-317 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider the nonlinear difference equation with several delays \[ (ax_{n+1}+bx_{n})^k-(cx_{n})^k+\sum \limits _{i=1}^{m} p_{i}(n)x^k_{n-\sigma _{i}}=0 \] where $a,b,c\in (0,\infty )$, $k=q/r, q, r$ are positive odd integers, $m$, $\sigma _{i}$ are positive integers, $\lbrace p_{i}(n)\rbrace $, $i=1,2,\dots ,m, $ is a real sequence with $p_{i}(n)\ge 0$ for all large $n$, and $\liminf _{n\rightarrow \infty }p_{i}(n)=p_{i}<\infty $, $i=1,2,\dots ,m$. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained. (English) |
| Keyword:
|
nonlinear difference equtions |
| Keyword:
|
oscillation |
| Keyword:
|
eventually positive solutions |
| Keyword:
|
characteristic equation |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1055.39015 |
| idMR:
|
MR2012607 |
| DOI:
|
10.21136/MB.2003.134176 |
| . |
| Date available:
|
2009-09-24T22:10:04Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134176 |
| . |
| 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:
|
[9] B. G. Zhang, Yong Zhou: Oscillation of delay differential equations with several delays.(to appear). |
| Reference:
|
[10] B. G. Zhang, Y. J. Sun: Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term.Math. Bohem. 126 (2001), 639–647. MR 1970266 |
| . |
