Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects

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 Allee effects in a seasonally varying environment. The Allee effect refers to a decrease in population growth rate at low population densities. Leggett–Williams multiple fixed point theorem is used to establish the existence of positive periodic solutions.