Open Access Research

The existence of eigenvalue problems for the waveguide theory

A Maher1* and EM Karachevskii2

Author Affiliations

1 Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

2 Department of Applied Mathematics, Kazan State University, 18 Kremlyovskaya st., Kazan, 420008, Russia

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Boundary Value Problems 2012, 2012:133 doi:10.1186/1687-2770-2012-133

Published: 13 November 2012

Abstract

In this paper, the existence of the eigenvalue problem for the waveguide theory is investigated. We used the Fourier transformation method for the solution of this problem. Also, we applied this problem to a dielectric waveguide. In this study, four theorems and two lemmas are obtained.

MSC: 35A22, 35P10.

Keywords:
partial differential equations; eigenvalue problems; Fourier transformation method