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The study of the possibility of existence of the non-propagating, trappedcontinental shelf waves (CSWs)along curved coasts reduces mathematically to aspectral problem for a self-adjoint operator pencil in a curved strip. Usingthe methods developed in the setting of the waveguide trapped mode problem, weshow that such CSWs exist for a wide class of coast curvature and depthprofiles.

Existence of Eigenvalues of a Linear Operator Pencil in a Curved Waveguide---Localized Shelf Waves on a Curved Coast