Positive periodic solutions of delayed differential equations

In this paper, we are concerned with the existence, multiplicity and nonexistence of positive ω-periodic solutions of the following equation.u″(t)+a(t,u)u(t)=λb(t)f(u(t-τ(t))),t∈R,where a(·,·)∈C(R×R,R+)a(·,·)∈C(R×R,R+) is a ω  -periodic function with respect to the first variable, b(·)∈C(R,[0,∞)),τ(·)∈C(R,R)b(·)∈C(R,[0,∞)),τ(·)∈C(R,R) all are ω-periodic functions, f ∈ C([0, ∞), [0, ∞)) and f(s) > 0 for s > 0. λ > 0 is a parameter. The proof of our main results is based upon fixed point index theory.