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

The existence results of positive ω-periodic solutionsare obtained for the second-order functional differential equation withmultiple delays u″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))),where a(t)∈C(ℝ) is a positive ω-periodic function, f:ℝ×[0,+∞)n+1→[0,+∞) is a continuous function which is ω-periodic in t, and τ1(t),…,τn(t)∈C(ℝ,[0,+∞)) are ω-periodic functions. The existence conditionsconcern the first eigenvalue of the associated linear periodicboundary problem. Our discussion is based on the fixed-point indextheory in cones