On a nonlinear eigenvalue problem related to the theory of propagation of electromagnetic waves

DOI10.1134/S0012266118020039zbMath1453.34031OpenAlexW2799991370WikidataQ129945737 ScholiaQ129945737MaRDI QIDQ721861

Dmitry V. Valovik

Publication date: 20 July 2018

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266118020039

zbMATH Keywords

discrete eigenvaluesnonlinear eigenvalue probleminfinite number of positive and negative eigenvalues

Mathematics Subject Classification ID

Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (7)

Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide. I: TE-TE waves ⋮ Study of a nonlinear eigenvalue problem by the integral characteristic equation method ⋮ Nonlinear multiparameter eigenvalue problems: linearised and nonlinearised solutions ⋮ Maxwell's equations in a plane waveguide with nonhomogeneous nonlinear permittivity: analytical and numerical approaches ⋮ Nonlinearized nonlinear electromagnetic guided waves in a circle cylindrical waveguide filled with nonlinear dielectric medium ⋮ Electromagnetic guided waves in a lossless cubic-quintic nonlinear waveguide ⋮ Multiparameter eigenvalue problems and their applications in electrodynamics

Cites Work

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• Guided electromagnetic waves propagating in a two-layer cylindrical dielectric waveguide with inhomogeneous nonlinear permittivity
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• Dual variational methods in critical point theory and applications
• Integral dispersion equation method to solve a nonlinear boundary eigenvalue problem
• On the infinitely many nonperturbative solutions in a transmission eigenvalue problem for Maxwell’s equations with cubic nonlinearity

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