Abstract
In this paper we shall consider the nonlinear delay differential equation (∗)p′(t)=β(t)pm(t−kω)1+pn(t−kω)−γ(t)p(t),where k is a positive integer, β(t) and γ(t) are positive periodic functions of period ω. In the nondelay case we shall show that (∗) has a unique positive periodic solution p̄(t), and we will study the global attractivity of p̄(t). In the delay case we shall establish some sufficient conditions for oscillation of all positive solutions of (∗) about p̄(t), and establish some sufficient conditions for the global attractivity of p̄(t). Our results in this paper extend as well as improve the results in the autonomous case.
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