Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map. (16th April 2014) - Ma, Tiantian; Wang, Zaihong
Abstract : 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.