Existence of eigenvalues of a linear operator pencil in a curved   waveguide -- localized shelf waves on a curved coast
  The study of the possibility of existence of the non-propagating, trapped continental shelf waves (CSWs)along curved coasts reduces mathematically to a spectral problem for a self-adjoint operator pencil in a curved strip. Using the methods developed in the setting of the waveguide trapped mode problem, we show that such CSWs exist for a wide class of coast curvature and depth profiles. 
E R Johnson, Michael Levitin, Leonid Parnovski