Positive periodic solutions of nonlinear functional differential equations

摘要

We apply the generalized form of Leggett–Williams fixed point theorem to prove that the following nonlinear functional differential equationx′(t)=−a(t)x(t)+f(t,xt)has at least two positive T-periodic solutions, where a(t) is a T-periodic function satisfying exp(∫0Ta(u)du)>1, f(t,xt) is a nonnegative function defined on R×BC, where BC denotes the Banach space of bounded continuous functions.