| Title:
|
Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term (English) |
| Author:
|
Zhang, B. G. |
| Author:
|
Sun, Y. J. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
639-647 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation \[ \Delta (x_{n}-p_{n} x_{\tau (n)})+f(n,x_{\sigma (n)})=q_{n} \] are obtained. Examples are included to illustrate the results. (English) |
| Keyword:
|
difference equations |
| Keyword:
|
nonlinear |
| Keyword:
|
forced term |
| Keyword:
|
nonoscillation |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 0982.39003 |
| idMR:
|
MR1970266 |
| DOI:
|
10.21136/MB.2001.134192 |
| . |
| Date available:
|
2009-09-24T21:55:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134192 |
| . |
| Reference:
|
[1] R. P. Agarwal: Difference Equations and Inequalities.Marcel Dekker, New York, 2000. Zbl 0952.39001, MR 1740241 |
| Reference:
|
[2] R. P. Agarwal, P. J. Y. Wong: Advanced Topics in Difference Equations.Kluwer, Dordrecht, 1997. MR 1447437 |
| Reference:
|
[3] M. P. Chen, B. G. Zhang: The existence of the bounded positive solutions of delay difference equations.PanAmerican Math. J. 3 (1993), 79–94. MR 1201542 |
| Reference:
|
[4] J. R. Graef, A. Miciano, P. W. Spikes, P. Sundaram, E. Thandapani: On the asymptotic behavior of solutions of a nonlinear difference equation.Proceedings of the First International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 223–229. MR 1678694 |
| Reference:
|
[5] J. R. Graef, A. Miciano, P. W. Spikes, P. Sundaram, E. Thandapani: Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations.J. Austral. Math. Soc. Ser. B 38 (1996), 163–171. MR 1414357, 10.1017/S0334270000000552 |
| Reference:
|
[6] J. R. Graef, P. W. Spikes: Boundedness and asymptotic behavior of solutions of a forced difference equations.Internat. J. Math. and Math. Sci. 17 (1994), 397–400. MR 1261087, 10.1155/S0161171294000542 |
| Reference:
|
[7] J. R. Graef, J. Jaros, A. Miciano, P. W. Spikes: Oscillation and nonoscillation results for nonlinear difference equations with a forcing term.Proceedings of the first International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 213–222. MR 1678690 |
| Reference:
|
[8] B. G. Zhang, H. Wang: The existence of nonoscillatory and oscillatory solutions of neutral difference equations.Dynam. Systems Appl. 6 (1997), 411–428. MR 1470829 |
| Reference:
|
[9] B. S. Lalli, B. G. Zhang: On existence of positive solutions and bounded oscillations for neutral difference equations.J. Math. Anal. Appl. 166 (1992), 272–287. MR 1159653, 10.1016/0022-247X(92)90342-B |
| Reference:
|
[10] B. S. Lalli, B. G. Zhang, J. Z. Li: On the oscillation of solutions and existence of positive solutions of neutral difference equations.J. Math. Anal. Appl. 158 (1991), 213–233. MR 1113411, 10.1016/0022-247X(91)90278-8 |
| Reference:
|
[11] E. Thandapani, J. R. Graef, P. W. Spikes: On existence of positive solutions and oscillations of neutral difference equations of odd order.J. Differ. Equations Appl. 2 (1996), 175–183. MR 1384567, 10.1080/10236199608808052 |
| Reference:
|
[12] Wudu Lu: Existence of nonoscillatory solutions of first order nonlinear neutral equations.J. Austral. Math. Soc. Ser. B 32 (1990), 180–192. Zbl 0723.34069, 10.1017/S0334270000008419 |
| Reference:
|
[13] B. G. Zhang, H. Wang: The existence of nonoscillatory and oscillatory solutions of neutral difference equations.Dynam. Systems Appl. 6 (1997), 411–428. MR 1470829 |
| . |
