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On the existence of infinitely many eigenvalues in a nonlinear Sturm–Liouville problem arising in the theory of waveguides

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Abstract

We consider a nonlinear eigenvalue problem of the Sturm–Liouville type on an interval with boundary conditions of the first kind. The problem describes the propagation of polarized electromagnetic waves in a plane two-layer dielectric waveguide. The cases of a homogeneous and an inhomogeneous medium are studied. The existence of infinitely many positive and negative eigenvalues is proved.

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Authors and Affiliations

  1. Penza State University, Penza, 440026, Russia

    V. Yu. Kurseeva & Yu. G. Smirnov

Authors
  1. V. Yu. Kurseeva
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  2. Yu. G. Smirnov
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Correspondence to V. Yu. Kurseeva.

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Original Russian Text © V.Yu. Kurseeva, Yu.G. Smirnov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 11, pp. 1453–1460.

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Kurseeva, V.Y., Smirnov, Y.G. On the existence of infinitely many eigenvalues in a nonlinear Sturm–Liouville problem arising in the theory of waveguides. Diff Equat 53, 1419–1427 (2017). https://doi.org/10.1134/S0012266117110040

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  • DOI: https://doi.org/10.1134/S0012266117110040

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