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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 4, Pages 261-270
http://dx.doi.org/10.1155/S0161171200001010

Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

Department of Basic Sciences, Naval Aeronautical Engineering Academy, Shandong, Yantai 264001, China

Received 19 June 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.