Abstract
The current paper clarifies the connection between the generalized complex-frequency eigenvalue problem and the corresponding nonlinear eigenvalue problem for the set of Muller integral equations posed on two disjoint closed curves. It is proved that the last problem has no solutions if the original problem and a specially tailored eigenvalue problem do not have solutions. This result is important for using the Muller boundary integral equations in the microring lasers theory.
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Repina, A.I., Oktyabrskaya, A.O. & Karchevskii, E.M. Muller Boundary Integral Equations in the Microring Lasers Theory. Lobachevskii J Math 42, 1402–1412 (2021). https://doi.org/10.1134/S199508022106024X
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DOI: https://doi.org/10.1134/S199508022106024X