Infinitely many cylindrically symmetric solutions of nonlinear Maxwell equations with concave and convex nonlinearities

DOI10.1007/s00033-022-01868-9zbMath1501.35386OpenAlexW4306318574MaRDI QIDQ2085805

Yanyun Wen, Pei-Hao Zhao

Publication date: 19 October 2022

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-022-01868-9

zbMATH Keywords

variational methodsMaxwell equationscritical exponentcylindrical symmetry solution

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Variational methods applied to PDEs (35A15) Critical exponents in context of PDEs (35B33) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Electromagnetic theory (general) (78A25) Variational methods for second-order elliptic equations (35J20)

Related Items (2)

Ground state solution of weakly coupled time-harmonic Maxwell equations ⋮ Multiple cylindrically symmetric solutions of nonlinear Maxwell equations

Cites Work

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• Time-harmonic Maxwell equations with asymptotically linear polarization
• Ground states of time-harmonic semilinear Maxwell equations in \(\mathbb R^3\) with vanishing permittivity
• Ground states of a nonlinear curl-curl problem in cylindrically symmetric media
• Nonlinear time-harmonic Maxwell equations in domains
• Magnetostatic solutions for a semilinear perturbation of the Maxwell equations
• Cylindrically symmetric ground state solutions for curl-curl equations with critical exponent
• The principle of symmetric criticality
• Existence of static solutions of the semilinear Maxwell equations
• Critical point theorems for indefinite functionals
• Guidance properties of nonlinear planar waveguides
• A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric
• The Brezis-Nirenberg problem for the curl-curl operator
• Existence and phase separation of entire solutions to a pure critical competitive elliptic system
• Towards a unified field theory for classical electrodynamics
• Local superlinearity and sublinearity for indefinite semilinear elliptic problems.
• Minimax theorems
• Infinitely many solutions of Dirac equations with concave and convex nonlinearities
• Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
• Multiple solutions to a nonlinear curl-curl problem in \({\mathbb{R}}^3\)
• Deformation in locally convex topological linear spaces
• Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium
• Time-Harmonic Maxwell Equations in the Exterior of Perfectly Conducting, Irregular Obstacles
• EXISTENCE OF GUIDED CYLINDRICAL TM-MODES IN AN INHOMOGENEOUS SELF-FOCUSING DIELECTRIC
• Deformation theorems on non-metrizable vector spaces and applications to critical point theory
• Singularities of Maxwell interface problems
• Vector potentials in three-dimensional non-smooth domains
• A Variational Problem Related to Self-trapping of an Electromagnetic Field
• Finite Element Methods for Maxwell's Equations
• Axisymmetric TE-Modes in a Self-focusing Dielectric

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