Abstract
An elementary method to prove the existence of odd periodic solutions with a prescribed number of zeros is presented. In some cases it is also possible to prove the uniqueness of this solution. The method combines shooting arguments with Sturm comparison theory and can be applied to a large class of nonlinear oscillators. In particular, this class includes the Sitnikov problem, a well-known restricted three body problem.
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Supported by MTM2014-52232-P, Spain and Dedicated to Professor Ernst-Ulrich Gekeler.
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Ortega, R. Symmetric periodic solutions in the Sitnikov problem. Arch. Math. 107, 405–412 (2016). https://doi.org/10.1007/s00013-016-0931-1
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DOI: https://doi.org/10.1007/s00013-016-0931-1