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Bull. Korean Math. Soc. 2007; 44(1): 177-184

Printed March 1, 2007

Copyright © The Korean Mathematical Society.

Asymptotic behavior of nonlinear Volterra difference systems

Sung Kyu Choi, Yoon Hoe Goo, and Nam Jip Koo

Chungnam National University, Hanseo University, Chungnam National University

Abstract

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We study the asymptotic behavior of nonlinear Volterra difference system $$ x(n+1)=f(n,x(n))+\sum_{s=n_0}^n g(n,s,x(s)),\;x(n_0)=x_0 $$ by using the resolvent matrix $R(n,m)$ of the corresponding linear Volterra system and the comparison principle.

Keywords: asymptotic equivalence, asymptotic equilibrium, nonlinear Volterra difference system, resolvent matrix, comparison principle

MSC numbers: 34D05, 34D23, 34E10, 39A11

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