This paper is devoted to the spectral theory (more precisely, to
the variational theory of the spectrum) of guided waves in an
elastic half cylinder. We use variational methods to investigate
several aspects of propagating waves, including localization (see
Figure 1), existence criteria and the formulas to find them. We
approach the problem using two complementary methods: The
variational methods for non-overdamped operator pencils to
describe eigenvalues in definite spectral zones, and
Ljusternik-Schnirelman critical point theory to investigate
eigenvalues in the mixed spectral zone where the classical
variational theory of operator pencils is not applicable.
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