Convergencia de soluciones positivas de una ecuación en diferencia no lineal

Abstract

This work discusses the convergence properties of positive solutions of the nonlinear difference equation in the case for β <1 + g (α) that is exposed in the MRS & S. Kulenovic Kalabusic article. On the Recursive Sequence x_(n+1)=α+(βx_(n.1))/(1+g(x_n)).Taylor & Francis Group. 2003. The development of this work being done by presenting a first chapter that shows basic concepts necessary for the understanding and study of the second chapter, definitions and theorems about sequences, subsequences, boundedness, convergence, theorem of Bolzano, completeness axiom, linear difference equations, nonlinear difference equations, equilibrium points. In the second chapter we present the study and reconstruction of the theorems about convergence of positive solutions presented in the article for the case β <1 + g (α), and answers the question whether every positive solution of equation converges to the positive equilibrium point. Finally in the third chapter there are some examples presented using GeoGebebra mathematical tool to visualize the convergence of positive solutions of the nonlinear equation in differences around equilibrium point.