Oscillating solutions for nonlinear Helmholtz equations

DOI10.1007/s00033-017-0859-8zbMath1383.35060arXiv1702.03727OpenAlexW2594322244MaRDI QIDQ680155

Benedetta Pellacci, Rainer Mandel, Eugenio Montefusco

Publication date: 22 January 2018

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

Full work available at URL: https://arxiv.org/abs/1702.03727

zbMATH Keywords

oscillating solutionsstanding wavesnonlinear Helmholtz equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (20)

Dual variational methods for a nonlinear Helmholtz system ⋮ Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases ⋮ The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations ⋮ Localization of normalized solutions for saturable nonlinear Schrödinger equations ⋮ Existence and multiplicity of solutions for a class of Helmholtz systems ⋮ On isolated singular solutions of semilinear Helmholtz equation ⋮ Oscillating solutions for nonlinear equations involving the Pucci's extremal operators ⋮ Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium ⋮ An annulus multiplier and applications to the limiting absorption principle for Helmholtz equations with a step potential ⋮ Existence and Asymptotics of Nonlinear Helmholtz Eigenfunctions ⋮ Existence and concentration of ground states for saturable nonlinear Schrödinger equations with intensity functions in \(\mathbb{R}^2\) ⋮ Uncountably many solutions for nonlinear Helmholtz and curl-curl equations ⋮ Bifurcations of nontrivial solutions of a cubic Helmholtz system ⋮ Dual ground state solutions for the critical nonlinear Helmholtz equation ⋮ Fourier extension estimates for symmetric functions and applications to nonlinear Helmholtz equations ⋮ Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity ⋮ Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime ⋮ On a fourth‐order nonlinear Helmholtz equation ⋮ Complex Solutions and Stationary Scattering for the Nonlinear Helmholtz Equation ⋮ Variational methods for breather solutions of nonlinear wave equations

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