On spectrum of a Schroedinger operator with a fast oscillating compactly   supported potential
  We study the phenomenon of an eigenvalue emerging from essential spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential. We prove the sufficient conditions for the existence and absence of such eigenvalue. If exists, we obtain the leading term of its asymptotics expansion. 
Denis I. Borisov, Rustem R. Gadyl'shin