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On positive periodic solutions to second-order differential equations with a sub-linear non-linearity. (English) Zbl 1458.34077

The authors study the existence and uniqueness of a positive periodic solution for a scalar equation of the type \[ u''=p(t)u-q(t,u). \] The general results can be applied to an equation of the type \[ u''=p(t)u-h(t)\sin u, \] where \(p(t)\) and \(h(t)\) are locally integrable periodic functions.

MSC:

34C25 Periodic solutions to ordinary differential equations
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