a variational approach to the problem of oscillations of an elastic half cylinder

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods for non-overdamped operator pencils todescribe eigenvalues in definite spectral zones, andljusternik-schnirelman critical point theory to investigateeigenvalues in the mixed spectral zone where the classicalvariational theory of operator pencils is not applicable.