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We study the periodic solutions of Duffing equations with singularities x′′+g(x)=p(t). By using Poincaré-Birkhoff twist theorem, we prove that the given equation possesses infinitely many positive periodic solutions provided that g satisfies the singular condition and the time map related to autonomous system x′′+g(x)=0 tends to zero

Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map