GLOBAL ATTRACTIVITY OF PERIODIC SOLUTIONS IN A DELAY DIFFERENTIAL EQUATION

摘要

Consider the following delay differential equation x'(t) = -a(t)x(t) + F(t, x(t - τ)), t ≥0 where a(t) : [0, ∞) → (0, ∞) is a continuous ω-periodic function, F(t, x) : [0, ∞) × [0, ∞) → (0, ∞) is a continuous function and an ω-periodic function in t, and τ ∈ (0, ∞) is a positive constant. We obtain a sufficient condition such that every positive solution of the equation converges to a positive periodic solution. Applications to some delay differential equation models derived from mathematical biology are also given.