| Title:
|
Asymptotic behavior of solutions of nonlinear difference equations (English) |
| Author:
|
Migda, Janusz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
349-359 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The nonlinear difference equation \[ x_{n+1}-x_n=a_n\varphi _n(x_{\sigma (n)})+b_n, \qquad \mathrm{(\text{E})}\] where $(a_n), (b_n)$ are real sequences, $\varphi _n\: \mathbb{R}\longrightarrow \mathbb{R}$, $(\sigma (n))$ is a sequence of integers and $\lim _{n\longrightarrow \infty }\sigma (n)=\infty $, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation $y_{n+1}-y_n=b_n$ are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained. (English) |
| Keyword:
|
difference equation |
| Keyword:
|
asymptotic behavior |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1080.39501 |
| idMR:
|
MR2102609 |
| DOI:
|
10.21136/MB.2004.134043 |
| . |
| Date available:
|
2009-09-24T22:16:11Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134043 |
| . |
| Reference:
|
[1] R. P. Agarwal: Difference Equations and Inequalities.Marcel Dekker, New York, 1992. Zbl 0925.39001, MR 1155840 |
| Reference:
|
[2] M. P. Chen, J. S. Yu: Oscillations for delay difference equations with variable coefficients.Proc. of the First International Conference of Difference Equations (1995), 105–114. MR 1678657 |
| Reference:
|
[3] S. S. Cheng, G. Zhang, S. T. Liu: Stability of oscillatory solutions of difference equations with delays.Taiwanese J. Math. 3 (1999), 503–515. MR 1730984, 10.11650/twjm/1500407163 |
| Reference:
|
[4] J. R. Graef, C. Qian: Asymptotic behavior of a forced difference equation.J. Math. Anal. Appl. 203 (1996), 388–400. MR 1410930, 10.1006/jmaa.1996.0387 |
| Reference:
|
[5] G. Ladas: Explicit conditions for the oscillation of difference equations.J. Math. Anal. Appl. 153 (1990), 276–287. Zbl 0718.39002, MR 1080131, 10.1016/0022-247X(90)90278-N |
| Reference:
|
[6] M. Migda, J. Migda: Asymptotic properties of the solutions of second order difference equation.Arch. Math. (Brno) 34 (1998), 467–476. MR 1679641 |
| Reference:
|
[7] E. Schmeidel: Asymptotic properties of solutions of a nonlinear difference equations.Comm. Appl. Nonlinear Anal. 4 (1997), 87–92. MR 1442100 |
| Reference:
|
[8] J. Shen, J. P. Stavroulakis: Oscillation criteria for delay difference equations.Electronic J. Differ. Eq. 10 (2001), 1–15. MR 1811783 |
| Reference:
|
[9] X. H. Tang, J. S. Yu: Oscillation of nonlinear delay difference equations.J. Math. Anal. Appl. 249 (2000), 476–490. Zbl 0963.39021, MR 1781236, 10.1006/jmaa.2000.6902 |
| Reference:
|
[10] X. H. Tang, Y. Liu: Oscillation for nonlinear delay difference equations.Tamkang J. Math. 32 (2001), 275–280. MR 1865621 |
| Reference:
|
[11] X. H. Tang, J. S. Yu: Oscillation of delay difference equations.Comput. Math. Appl. 37 (1999), 11–20. Zbl 0976.39005, MR 1729819, 10.1016/S0898-1221(99)00083-8 |
| Reference:
|
[12] J. Yan, C. Qian: Oscillation and comparison results for delay difference equations.J. Math. Anal. Appl. 165 (1992), 346–360. MR 1155726, 10.1016/0022-247X(92)90045-F |
| . |
