Asymptotic analysis of a nonlinear eigenvalue problem arising in the waveguide theory

DOI10.1134/S0012266119120036zbMath1444.34042OpenAlexW3005519663MaRDI QIDQ2187843

Dmitry V. Valovik, S. V. Tikhov

Publication date: 3 June 2020

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

Full work available at URL: https://doi.org/10.1134/s0012266119120036

Mathematics Subject Classification ID

Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Parameter dependent boundary value problems for ordinary differential equations (34B08) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (2)

Propagation of electromagnetic waves in an open planar dielectric waveguide filled with a nonlinear medium. II: TM waves ⋮ Maxwell's equations with arbitrary self-action nonlinearity in a waveguiding theory: guided modes and asymptotic of eigenvalues

Cites Work

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• Characteristic values associated with a class of nonlinear second-order differential equations
• On the existence of infinitely many eigenvalues in a nonlinear Sturm-Liouville problem arising in the theory of waveguides
• On the existence of an infinite number of eigenvalues in one nonlinear problem of waveguide theory
• 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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