Existence and global attractivity of unique positive periodic solution for a Lasota-Wazewska model

Abstract

In this paper we consider the Lasota-Wazewska modelx′(t)=-a(t)x(t)+∑i=1mpi(t)e-qi(t)x(t-τi(t)).By using a fixed point theorem, some criteria are established for the existence of the unique positive ω-periodic solution x̃ of the above equation. In particular, we not only give the conclusion of convergence of xn to x̃, where {xn} is a successive sequence, but also show that x̃ is a global attractor of all other positive solutions. © 2005 Elsevier Ltd. All rights reserved.