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A forced pendulum equation with many periodic solutions. (English) Zbl 0899.34031

The author shows that if \(a\) is a positive real number and \(n\) an integer greater than or equal to \(1\), then there exists \(p(t)\) satisfying \(p\in L^1(\mathbb{R}/T\mathbb{Z})\), and \(\int^T_0 p(t)dt= 0\), such that the forced pendulum equation \(x''+ a\sin x= p(t)\) has at least \(2n\) \(T\)-periodic solutions which are geometrically different.
Reviewer: O.Akinyele (Bowie)

MSC:

34C25 Periodic solutions to ordinary differential equations
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References:

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