Addenda to “Periodic solutions of with arbitrarily large period”
The asymptotic behaviour of a Sturm-Liouville differential equation with coefficient is investigated, where and is a nondecreasing step function tending to as . Let denote the set of those ’s for which the corresponding differential equation has a solution not tending to 0. It is proved that is an additive group. Four examples are given with , , (i.e. the set of dyadic numbers), and .