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The phase-integral method in a problem of singular perturbation theory

This paper is devoted to the development of the phase-integral method as applied to a boundary- value problem modelling the passage from discrete to continuous spectrum in the non- selfadjoint case. Our aim is to study the patterns and features of the asymptotic distribution of eigenvalues of the problem and to describe the topologically distinct types of spectrum configurations in the quasiclassical limit.