Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane
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Publication:2628094
DOI10.1515/anly-2016-0023zbMath1376.35004arXiv1606.00788OpenAlexW2962699658MaRDI QIDQ2628094
Publication date: 12 June 2017
Published in: Analysis (München) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.00788
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)
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Cites Work
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- Nonlinear scalar field equations. II: Existence of infinitely many solutions
- Nonlinear scalar field equations. I: Existence of a ground state
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- A dual approach in Orlicz spaces for the nonlinear Helmholtz equation
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
- Existence of solutions for semilinear elliptic equations with indefinite linear part
- Entire solutions of semilinear elliptic equations
- Non trivial \(L^q\) solutions to the Ginzburg-Landau equation
- Elliptic partial differential equations of second order
- Inverse problem for a nonlinear Helmholtz equation
- Minimax theorems
- Dual variational methods in critical point theory and applications
- Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
- Real solutions to the nonlinear Helmholtz equation with local nonlinearity
- Uniqueness of radiative solutions to the Schrödinger wave equation
- Spectral and scattering theory for Schrödinger operators
- Growth properties of solutions of the reduced wave equation with a variable coefficient
- Variational Methods
- Inverse acoustic and electromagnetic scattering theory
- A restriction theorem for the Fourier transform