Infinitely many periodic solutions of Duffing equations with singularities via time map. (English) Zbl 1470.34120

Ma, Tiantian; Wang, Zaihong

Abstr. Appl. Anal. 2014, Article ID 398512, 8 p. (2014).

Summary: 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.

MSC:

34C25	Periodic solutions to ordinary differential equations
34B16	Singular nonlinear boundary value problems for ordinary differential equations

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