On Some Specific Non-Linear Ordinary Difference Equations

Eugenia N. Petropoulou

E-mail: jenny@math.upatras.gr

Abstract. It is proved that some specific non-linear ordinary difference equations, which appear in various applications, have a unique solution in the Banach space $l_{1}$. Moreover a bound of the solutions and a region of attraction of their equilibrium points are found. The obtained results improve some previous known results.

AMSclassification. 32H02, 39A10, 39A11

Keywords. Non-linear difference equations, bounded solutions, asymptotic stability