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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:
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


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