Periodic solutions of first order functional differential equations with periodic deviations

The paper is concerned with the functional differential equation u′(t)=a(t)g(u(h1(t)))u(t)−λb(t)f(u(h2(t))),u′(t)=a(t)g(u(h1(t)))u(t)−λb(t)f(u(h2(t))), where λ>0,a(t),b(t),h1(t)λ>0,a(t),b(t),h1(t) and h2(t)h2(t) are periodic functions. Applying Leggett–Williams fixed point theorem to the equation, we show the explicit open intervals of λλ such that the equation has at least three nonnegative periodic solutions.