| Title:
|
Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation (English) |
| Author:
|
Thandapani, E. |
| Author:
|
Ramuppillai, L. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
[499]-506 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma <1)$. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
nonlinear delay difference equation |
| Keyword:
|
Emden-Fowler type |
| MSC:
|
34K40 |
| MSC:
|
39A05 |
| MSC:
|
39A10 |
| MSC:
|
39A12 |
| MSC:
|
39A21 |
| idZBL:
|
Zbl 1274.39022 |
| idMR:
|
MR1723577 |
| . |
| Date available:
|
2009-09-24T19:27:39Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135304 |
| . |
| Reference:
|
[1] Agarwal R. P.: Difference Equations and Inequalities.Marcel Dekker, New York 1992 Zbl 0952.39001, MR 1155840 |
| Reference:
|
[2] Gaef J. R., Spikes P. W.: Boundedness and asymptotic behavior of solutions of a forced difference equation.Internat. J. Math. Math. Sci. 17 (1994), 397–400 MR 1261087, 10.1155/S0161171294000542 |
| Reference:
|
[3] Gaef J. R., Spikes P. W.: Asymptotic decay of oscillatory solutions of forced nonlinear difference equations.Dynamic Systems Appl. 3 (1994), 95–102 MR 1261052 |
| Reference:
|
[4] Hooker J. W.: Some differences between difference equations and differential equations.J. Differential Equations Appl. 2 (1996), 219–226 Zbl 0856.34036, MR 1384571, 10.1080/10236199608808056 |
| Reference:
|
[5] Hooker J. W., Patula W. T.: A second order nonlinear difference equation: oscillation and asymptotic behavior.J. Math. Anal. Appl. 91 (1983), 9–29 Zbl 0508.39005, MR 0688528, 10.1016/0022-247X(83)90088-4 |
| Reference:
|
[6] Kordonis I. G. E., Philos, Ch. G., Purnaras I. K.: On the oscillation of some linear difference equations with periodic coefficients.J. Comput. Appl. Math. 84 (1997), 219–241 Zbl 0885.39006, MR 1475376, 10.1016/S0377-0427(97)00126-X |
| Reference:
|
[7] Lakshmikantham V., Trigiante D.: Theory of Difference Equations: Numerical Methods and Applications.Academic Press, New York 1988 Zbl 1014.39001, MR 0939611 |
| Reference:
|
[8] Moore R. E.: Computational Functional Analysis.(Ellis Harwood Series.) Halstred Press, New York 1985 Zbl 1127.46001, MR 0783431 |
| Reference:
|
[9] Patula W. T.: Growth, oscillation and comparison theorems for second order linear difference equation.SIAM J. Math. Anal. 10 (1979), 1272–1279 MR 0547812, 10.1137/0510114 |
| Reference:
|
[10] Popenda J.: On the oscillation of solutions of difference equations.Demonstratio Math. 28 (1995), 575–586 Zbl 0846.39006, MR 1362187 |
| Reference:
|
[11] Szmanda B.: Nonoscillation, oscillation and growth of solutions of nonlinear difference equations of second order.J. Math. Anal. Appl. 109 (1985), 22–30 Zbl 0589.39003, MR 0796040, 10.1016/0022-247X(85)90174-X |
| Reference:
|
[12] Thandapani E., Pandian S.: On the oscillatory behavior of solutions of second order nonlinear difference equation.Z. Anal. Anwendungen 13 (1993), 347–358 |
| Reference:
|
[13] Thandapani E., Ramuppillai L.: Oscillation theorems for certain class of nonlinear difference equations.Z. Anal. Anwendungen 17 (1998), 1–10 Zbl 0906.39008, MR 1632500, 10.4171/ZAA/836 |
| Reference:
|
[14] Zafer A.: On the existence of positive solutions and oscillation of solutions of higher order differenced equations with forcing terms.Comput. Math. Appl., to appear MR 1666123 |
| Reference:
|
[15] Zhang B. G.: 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 |
| . |
