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The existence results of positive ω-periodic solutions are obtained for the second-order ordinary differential equation u′′(t)=f(t,u(t),u'(t)),t∈ℝ where, f:ℝ×(0,∞)×ℝ→ℝ is a continuous function, which is ω-periodic in t and f(t,u,v) may be singular at u=0. The discussion is based on the fixed point index theory in cones

Positive Periodic Solutions for Second-Order Ordinary Differential Equations with Derivative Terms and Singularity in Nonlinearities