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

Abstract

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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.

How to cite

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Petropoulou, 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

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  1. On the difference equation x n + 1 = 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. 
  2. 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
  3. 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
  4. Stability theory for difference equations, In: Studies in Mathematics, Vol.14 (1977), 1–31, Math. Assoc. America. Zbl0397.39009MR0481689
  5. Global attractivity in a nonlinear difference equation, Applied Mathematics and Computation, Vol. 62 (1994), 249–258. MR1284547

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