Abstract:
In this article the minimum number of positive periodic solutions admitted
by a non-autonomous scalar differential equation is estimated. This result is employed to
find the minimum number of positive periodic solutions admitted by a model representing
dynamics of a renewable resource that is subjected to additive Allee effects in a seasonally
varying environment. Leggett-Williams multiple fixed point theorem is used to establish
the existence of at least two positive periodic solutions for the considered dynamic equation.
Two methods are obtained to establish the existence of periodic solutions. Key
results are illustrated through numerical simulation.
