On positive periodic solutions to second-order differential equations with a sub-linear non-linearity (Q2215492)

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.