Periodic solutions and oscillation of discrete non-linear delay population dynamics model with external force

Abstract

where m is a positive integer, p(n), Q(n) and λ(n) are positive periodic sequences of period ω. By the method that involves the application of the Gaines and Mawhins coincidence degree theory, we prove that there exists a positive ω-periodic solution ¯ y(n). We prove that every positive solution of (∗) which does not oscillate about ¯(n) satisfies limt→∞(y(n) −¯ y(n)) = 0. We establish some necessary and sufficient conditions for the oscillation of every positive solution about ¯ y(n), and finally, we establish the lower and upper bounds of the oscillatory solutions.