Solutions to a nonlinear Maxwell equation with two competing nonlinearities in $\mathbb{R}^3$

DOI10.4064/ba210731-19-8zbMath1483.35235arXiv2010.02000OpenAlexW3201778012MaRDI QIDQ5035320

Bartosz Bieganowski

Publication date: 21 February 2022

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.02000

zbMATH Keywords

nonlinear Schrödinger equationvariational methodsMaxwell equationssingular potentialsign-changing nonlinearities

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Critical exponents in context of PDEs (35B33) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Electromagnetic theory (general) (78A25) Variational methods for second-order elliptic equations (35J20)

Related Items (6)

Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities ⋮ Elliptic problems with mixed nonlinearities and potentials singular at the origin and at the boundary of the domain ⋮ Multiple cylindrically symmetric solutions of nonlinear Maxwell equations ⋮ On the ground states for the X‐ray free electron lasers Schrödinger equation ⋮ Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree-Fock theory ⋮ Ground state solutions and periodic solutions with minimal periods to second-order Hamiltonian systems

Cites Work

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• An improved Fountain theorem and its application
• Nonlinear Schrödinger equations with sum of periodic and vanishing potentials and sign-changing nonlinearities
• Finite Element Methods for Maxwell's Equations
• Nonradial solutions of nonlinear scalar field equations
• Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term

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