Resonances for multistratified acoustic waveguides

The equation of acoustic oscillations in multistratified waveguides is considered. It is assumed that the properties of the medium do not depend on the longitudinal coordinate in a neighbourhood of infinity and may be different at different ends of the waveguides. It is proved that the truncated resolvent of the corresponding operator admits an analytical continuation through the continuous spectrum. The singularities (poles, branching points) of the truncated resolvent on the continuous spectrum are investigated. The large time asymptotic behavior of the compulsory oscillations due to periodic forces is obtained.