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

Eugenia N. Petropoulou and Panayiotis D. Siafarikas

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 $l_{1}$