  We consider Sturm-Liouville operators with measure-valued weight and
potential, and positive, bounded diffusion coefficient which is bounded away
from zero. By means of a local periodicity condition, which can be seen as a
quantitative Gordon condition, we prove a bound on eigenvalues for the
corresponding operator in $L_p$, for $1\leq p<\infty$. We also explain the
sharpness of our quantitative bound, and provide an example for quasiperiodic
operators.
