Existence of three periodic solutions for a nonlinear first order functional differential equation

In this paper, we use Leggett–Williams multiple fixed point theorem to obtain different sufficient conditions for the existence of at least three nonnegative periodic solutions of the first order functional differential equation of the form y ′ ( t ) = - a ( t ) y ( t ) + λ f ( t , y ( h ( t ) ) ) . Some applications to mathematical ecological models are given.