On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

The existence results of positive omega-periodic solutions are obtained for the second-order functional differential equation with multiple delays u ''(t) + a(t)u(t) = f(t, u(t), u(t - tau(1)(t)), ..., u(t - tau(n)(t))), where a(t) is an element of C(R) is a positive omega-periodic function, f : R x [0, +infinity)(n+1) -> [0, +infinity) is a continuous function which is omega-periodic in t, and tau(1)(t), ..., tau(n)(t) is an element of C(R, [0, +infinity)) are omega-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.