Asymptotic behavior of eigenvalues of Schr\"odinger type operators with degenerate kinetic energy

We study the eigenvalues of Schr"odinger type operators $T + \lambda V$andtheirasymptoticbehaviorinthesmallcouplinglimit$\lambda \to 0$,inthecasewherethesymbolofthekineticenergy,$T(p)$, strongly degenerates on a non-trivial manifold of codimension one.