Existence and global attractivity of unique positive periodic solution for a Lasota–Wazewska model Original Research Article

In this paper we consider the Lasota–Wazewska model View the MathML sourcex′(t)=-a(t)x(t)+∑i=1mpi(t)e-qi(t)x(t-τi(t)). Turn MathJax on By using a fixed point theorem, some criteria are established for the existence of the unique positive ωω-periodic solution View the MathML sourcex˜ of the above equation. In particular, we not only give the conclusion of convergence of xnxn to View the MathML sourcex˜, where {xn}{xn} is a successive sequence, but also show that View the MathML sourcex˜ is a global attractor of all other positive solutions.