Incomplete comparison principle in problems about surface waves trapped by fixed and freely floating bodies

We consider problems about interaction of surface waves with fixed and freely floating bodies. We propose a new boundary value problem with integro-differential boundary conditions. This problem has physical sense only in the case of a totally submerged body, but, in the case of symmetry in the geometric or physical sense, the nonemptiness of its discrete spectrum provides the existence of eigenvalues of both problems for a fixed body and a freely floating body (in the last case, under some additional requirements which make the comparison principle incomplete). Bibliography: 25 titles. Illustrations: 5 figures. © 2011 Springer Science+Business Media, Inc.