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

الملخص EN

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.