| Title:
|
On the oscillation of certain difference equations (English) |
| Author:
|
Grace, S. R. |
| Author:
|
El-Morshedy, H. A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
421-430 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the oscillation of the difference equations of the form
\Delta^2x_n+p_n\Delta x_n+f(n, x_{n-g}, \Delta x_{n-h})=0,
in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation
\Delta^2x_n+p_n\Delta x_n+q_n|x_{n-g}|^{\lambda}|\Delta x_{n-h}|^{\mu}\sgn x_{n-g}=0,
where $\lambda$ and $\mu$ are real constants, $\lambda>0$ and $\mu\geq0$. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
delay difference equations |
| Keyword:
|
forced equations |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
39A12 |
| idZBL:
|
Zbl 0969.39005 |
| idMR:
|
MR1802291 |
| DOI:
|
10.21136/MB.2000.126277 |
| . |
| Date available:
|
2009-09-24T21:45:10Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126277 |
| . |
| Reference:
|
[1] S. R. Grace: Oscillatory and asymptotic behavior of delay differential equations with a nonlinear damping term.J. Math. Anal. Appl. 168 (1992), 306-318. Zbl 0769.34049, MR 1175990, 10.1016/0022-247X(92)90159-B |
| Reference:
|
[2] S. R. Grace: Oscillation theorems of comparison type of delay differential equations with a nonlinear damping term.Math. Slovaca 44 (1994), no. 3, 303-314. Zbl 0815.34061, MR 1307320 |
| Reference:
|
[3] S. R. Grace B. S. Lalli: An oscillation criterion for certain second order strongly sublinear dífferential equations.J. Math. Anal. Appl. 123 (1987), 584-586. MR 0883711, 10.1016/0022-247X(87)90333-7 |
| Reference:
|
[4] S. R. Grace B. S. Lalli: Oscillation theorems for second order delay and neutrał difference equations.Utilitas. Math. 45 (1994), 197-211. MR 1284030 |
| Reference:
|
[5] S. R. Grace B. S. Lalli: Oscillation theorems for forced neutral difference equations.J. Math. Anal. Appl. 187 (1994), 91-106. MR 1296607, 10.1006/jmaa.1994.1346 |
| Reference:
|
[6] I. Györi G. Ladas: Oscillation Theory of Delay Differential Equations with Applications.Oxford Univ., Oxford, 1991. MR 1168471 |
| Reference:
|
[7] J. W. Hooker W. T. Patula: A second order nonlinear difference equations: Oscillation and asymptotic behavior.J. Math. Anal. Appl. 91 (1983), 9-29. MR 0688528, 10.1016/0022-247X(83)90088-4 |
| Reference:
|
[8] G. Ladas C. Qian: Comparison results and linearized oscillations for higher order difference equations.Internt. J. Math. Math. Sci. 15 (1992), 129-142. MR 1143937, 10.1155/S0161171292000152 |
| Reference:
|
[9] B. G. Zhang: Oscillation and asymptotic behavior of second order difference equations.J. Math. Anal. Appl. 173 (1993), 58-68. Zbl 0780.39006, MR 1205909, 10.1006/jmaa.1993.1052 |
| . |
