We consider the standard Sturm-Liouville eigenvalue problem Lu + λR(x)u = 0 in J = [0,T] with u(0)= Su(T),(u)(0)= S(u)(T)for some orthogonal matrix S,where Lu=(P(x)u)+Q(x)u+R0(x)u.Based on works of the Hill-type formula,we get a trace formula which can be considered as a generalization of Kreins work in 1950s,from which ∑1/λkj could computed for any natural number k.Some applications for the stability problem in n-body problem is given.This is based on joint works with Yuwei Ou and Penghui Wang.