# A forced pendulum equation without stable periodic solutions of a fixed period

### Rafael Ortega

Universidad de Granada, Spain

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## Abstract

The pendulum equation is forced by a continuous and $T$-periodic function with zero average. In these conditions it is well known that there exist at least two $T$-periodic solutions. We construct some examples where there are exactly two $T$-periodic solutions and both are unstable.

## Cite this article

Rafael Ortega, A forced pendulum equation without stable periodic solutions of a fixed period. Port. Math. 71 (2014), no. 3, pp. 193–216

DOI 10.4171/PM/1950