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Existence of positive periodic solutions of second-order differential equations with weak singularities

We establish the existence of positive periodic solutions of the second-order differential equation x ″ + a ( t ) x = f ( t , x ) + c ( t ) via Schauder’s fixed point theorem, where a ∈ L 1 ( R / T Z ; R + ) , c ∈ L 1 ( R / T Z ; R ) , f is a Caratheodory function and it is singular at x = 0 . Our main results generalize some recent results by Torres (J. Differ. Equ. 232:277-284...