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

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*Eugenia N. Petropoulou and Panayiotis D. Siafarikas*

**Address.** Department of Mathematics, University of Patras, Patras,
GREECE
**E-mail:** panos@math.upatras.gr

**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.

**AMSclassification.** 32H02, 39A10, 39A11

**Keywords.** Nonlinear difference equations, solution in $l_{1}$