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# Article

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Keywords:
nonlinear difference equations; solution in $l_{1}$
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.
References:
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[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
[4] LaSalle, J. P.: Stability theory for difference equations. In: Studies in Mathematics, Vol.14 (1977), 1–31, Math. Assoc. America. MR 0481689 | Zbl 0397.39009
[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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