# Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane

Eugenia N. Petropoulou; Panayiotis D. Siafarikas

Archivum Mathematicum (2000)

- Volume: 036, Issue: 2, page 139-158
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topPetropoulou, Eugenia N., and Siafarikas, Panayiotis D.. "Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane." Archivum Mathematicum 036.2 (2000): 139-158. <http://eudml.org/doc/248522>.

@article{Petropoulou2000,

abstract = {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.},

author = {Petropoulou, Eugenia N., Siafarikas, Panayiotis D.},

journal = {Archivum Mathematicum},

keywords = {nonlinear difference equations; solution in $l_\{1\}$; nonlinear difference equations; solution in ; bounded solution; asymptotic stability},

language = {eng},

number = {2},

pages = {139-158},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane},

url = {http://eudml.org/doc/248522},

volume = {036},

year = {2000},

}

TY - JOUR

AU - Petropoulou, Eugenia N.

AU - Siafarikas, Panayiotis D.

TI - Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane

JO - Archivum Mathematicum

PY - 2000

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 036

IS - 2

SP - 139

EP - 158

AB - 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.

LA - eng

KW - nonlinear difference equations; solution in $l_{1}$; nonlinear difference equations; solution in ; bounded solution; asymptotic stability

UR - http://eudml.org/doc/248522

ER -

## References

top- On the difference equation ${x}_{n+1}=\frac{{x}_{n}+{x}_{n-1}{x}_{n-2}}{{x}_{n}{x}_{n-1}+{x}_{n-2}}$, preprint, Department of Math., University of Rhode Island, U.S.A., March 20, 1998.
- 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. MR0266009
- On the convergence of Power-Series Whose Coefficients Satisfy a Poincaré-Type Linear and Nonlinear Difference Equation, Complex Variables, Vol. 9 (1987), 63–80. MR0916917
- Stability theory for difference equations, In: Studies in Mathematics, Vol.14 (1977), 1–31, Math. Assoc. America. Zbl0397.39009MR0481689
- Global attractivity in a nonlinear difference equation, Applied Mathematics and Computation, Vol. 62 (1994), 249–258. MR1284547

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.