Almost Periodic Solutions of Lasota-Wazewska-type Delay Differential Equation

Abstract

Sufficient conditions are derived for the existence of a globally attractive almost periodic solution of a single species model given by the nonautonomous Lasota-Wazewska-type delay differential equations,x′t=-δtxt+ptfxt-τ,in which τ0, p(t)≥0, δ(t) are continuous almost periodic functions, and f is a decreasing positive C1-function. Conditions of the uniform asymptotical stability for some associated nonautonomous delay differential equations,x′t=-δtxt+ptxt-τ,are also discussed. © 1999 Academic Press.