Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
From MaRDI portal
Publication:2257785
DOI10.1007/s00205-014-0778-1zbMath1315.35214arXiv1310.4731OpenAlexW3102811044MaRDI QIDQ2257785
Thomas J. Bartsch, Jarosław Mederski
Publication date: 2 March 2015
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1310.4731
Related Items (40)
Solutions to a nonlinear Maxwell equation with two competing nonlinearities in $\mathbb{R}^3$ ⋮ Nonlinear time-harmonic Maxwell equations in a bounded domain: lack of compactness ⋮ Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials ⋮ Ground state solutions for a class of semilinear elliptic systems with sum of periodic and vanishing potentials ⋮ Time-harmonic Maxwell equations with asymptotically linear polarization ⋮ Bound states for the Schroedinger equation with mixed-type nonlinearities ⋮ Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities ⋮ Solutions on asymptotically periodic elliptic system with new conditions ⋮ Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium ⋮ Nonlinear Schrödinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems without the Ambrosetti-Rabinowitz condition ⋮ Cylindrically symmetric solutions of curl-curl equation with nonlocal nonlinearity ⋮ Multiple Solutions to Cylindrically Symmetric Curl-Curl Problems and Related Schrödinger Equations with Singular Potentials ⋮ Ground state solution of weakly coupled time-harmonic Maxwell equations ⋮ Periodic solutions for second-order even and noneven Hamiltonian systems ⋮ Existence solution for curl-curl Kirchhoff problem ⋮ The Brezis-Nirenberg problem for the curl-curl operator ⋮ Travelling waves for Maxwell's equations in nonlinear and nonsymmetric media ⋮ Existence and nonexistence of solutions for p(x)-curl systems arising in electromagnetism ⋮ Geometrically distinct solutions of nonlinear elliptic systems with periodic potentials ⋮ Maxwell-Stokes system with \(L^2\) boundary data and div-curl system with potential ⋮ Ground states of time-harmonic semilinear Maxwell equations in \(\mathbb R^3\) with vanishing permittivity ⋮ Nonlinear curl-curl problems in $\mathbb{R}^3$ ⋮ Cylindrically symmetric ground state solutions for curl-curl equations with critical exponent ⋮ Solutions of the fractional Schrödinger equation with a sign-changing nonlinearity ⋮ Ground states of a nonlinear curl-curl problem in cylindrically symmetric media ⋮ Nonlinear time-harmonic Maxwell equations in domains ⋮ Existence of two solutions for \(p(x)\)-curl systems with a small perturbation ⋮ Ground state solutions for resonant cooperative elliptic systems with general superlinear terms ⋮ The fractional Schrödinger equation with Hardy-type potentials and sign-changing nonlinearities ⋮ Existence and multiplicity of solutions for \(p(x)\)-curl systems arising in electromagnetism ⋮ Ground state solutions for semilinear time-harmonic Maxwell equations ⋮ A Sobolev-type inequality for the curl operator and ground states for the curl-curl equation with critical Sobolev exponent ⋮ Multiple solutions to a nonlinear curl-curl problem in \({\mathbb{R}}^3\) ⋮ Variational and operator methods for Maxwell-Stokes system ⋮ Ground states of a system of nonlinear Schrödinger equations with periodic potentials ⋮ Existence and multiplicity of solutions for semilinear elliptic systems with periodic potential ⋮ Infinitely many cylindrically symmetric solutions of nonlinear Maxwell equations with concave and convex nonlinearities ⋮ Ground state solutions and periodic solutions with minimal periods to second-order Hamiltonian systems ⋮ Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Magnetostatic solutions for a semilinear perturbation of the Maxwell equations
- Photonic crystals. Mathematical analysis and numerical approximation.
- Modelling axi-symmetric travelling waves in a dielectric with nonlinear refractive index
- Periodic nonlinear Schrödinger equation with application to photonic crystals
- Existence of static solutions of the semilinear Maxwell equations
- Ground state solutions for some indefinite variational problems
- Critical point theorems for indefinite functionals
- Self-trapping of an electromagnetic field and bifurcation from the essential spectrum
- Deformation properties for continuous functionals and critical point theory
- A constrained minimization problem and its application to guided cylindrical TM-modes in an anisotropic self-focusing dielectric
- Towards a unified field theory for classical electrodynamics
- Minimax theorems
- Generalized linking theorem with an application to a semilinear Schrödinger equation
- 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
- 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
- Infinitely many solutions of a symmetric Dirichlet problem
- Variational Methods
- Axisymmetric TE-Modes in a Self-focusing Dielectric
- Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric
This page was built for publication: Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
