Abstract
Considering the example of a mixed boundary value problem for the Helmholtz operator we discuss two methods for finding eigenvalues below the continuous spectrum threshold: one variational and the other—asymptotic. We construct asymptotics for the eigenvalue arising near the threshold as a small obstacle appears in the cylindrical waveguide. The resulting asymptotic formula, its derivation and justification differ substantially from the case of a bounded domain.
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Original Russian Text Copyright © 2010 Nazarov S. A.
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 5, pp. 1086-1101, September-October, 2010
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Nazarov, S.A. Variational and Asymptotic Methods for Finding Eigenvalues below the Continuous Spectrum Threshold. Sib Math J 51, 866–878 (2010). https://doi.org/10.1007/s11202-010-0087-3
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DOI: https://doi.org/10.1007/s11202-010-0087-3