Trace estimation of a family of periodic Sturm-Liouville operators with application to Robe's restricted three-body problem

Abstract

In this paper, we consider a family of Sturm-Liouville operators on the $\omega$-periodic domain. The bifurcation with respect to the parameter region is studied, and the elliptic regions are estimated by trace formula. At last, these results are used to study the linear stability of the elliptic equilibrium point along $z$-axis in Robe's restricted three-body problem.