| Title:
|
Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane (English) |
| Author:
|
Petropoulou, Eugenia N. |
| Author:
|
Siafarikas, Panayiotis D. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
139-158 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An existence and uniqueness theorem for solutions in the Banach space $l_{1}$ of a nonlinear difference equation is given. The constructive character of the proof of the theorem predicts local asymptotic stability and gives information about the size of the region of attraction near equilibrium points. (English) |
| Keyword:
|
nonlinear difference equations |
| Keyword:
|
solution in $l_{1}$ |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
65Q05 |
| idZBL:
|
Zbl 1053.39016 |
| idMR:
|
MR1761618 |
| . |
| Date available:
|
2008-06-06T22:25:35Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107726 |
| . |
| Reference:
|
[1] Amleh, A. M., Kruse, N. and Ladas, G.: On the difference equation $x_{n+1}={x_{n}+x_{n-1}x_{n-2}\over x_{n}x_{n-1}+x_{n-2}}$.preprint, Department of Math., University of Rhode Island, U.S.A., March 20, 1998. |
| Reference:
|
[2] Earle, C. J. and Hamilton, R. S.: A fixed point theorem for holomorphic mappings.In: Global Analysis Proceedings Symposium Pure Mathematics, Vol. XVI, Berkeley, California, 1968, 61–65, American Mathematical Society, Providence, R.I., 1970. MR 0266009 |
| Reference:
|
[3] Ifantis, E. K.: On the convergence of Power-Series Whose Coefficients Satisfy a Poincaré-Type Linear and Nonlinear Difference Equation.Complex Variables, Vol. 9 (1987), 63–80. MR 0916917 |
| Reference:
|
[4] LaSalle, J. P.: Stability theory for difference equations.In: Studies in Mathematics, Vol.14 (1977), 1–31, Math. Assoc. America. Zbl 0397.39009, MR 0481689 |
| Reference:
|
[5] Philos, Ch., Purnaras, I. K. and Sficas, Y. G.: Global attractivity in a nonlinear difference equation.Applied Mathematics and Computation, Vol. 62 (1994), 249–258. MR 1284547 |
| . |
