## 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

### Keywords:

periodic solutions; bifurcation; forced pendulum equation
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### References:

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