Nonlinear scalar field equations, II existence of infinitely many solutions

1983/12/01 by H. Berestycki, Henri Berestycki, P. -L. Lions +1 · 802 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical mechanics #Complex system #Computer science #Cosmology and Gravitation Theories #Field (mathematics) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Scalar (mathematics) #Scalar field

paper · open access · doi:10.1007/bf00250556

published in Archive for Rational Mechanics and Analysis 82(4), 347-375 (Springer Science+Business Media)

openalex publication_date 1983/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Cited by

• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• Another look at Schrödinger equations with prescribed mass
• Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
• Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
• Multiple normalized solutions for a Sobolev critical Schrödinger equation
• Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth
• On the ill-posedness of some canonical dispersive equations
• Existence and asymptotics of nonlinear Helmholtz eigenfunctions
• Point interactions and singular solutions to semilinear elliptic equations
• Resolving Sharp Gradients of Unstable Singularities to Machine Precision via Neural Networks
• Construction of solitary wave solution of the nonlinear focusing schrödinger equation outside a strictly convex obstacle for the L²-supercritical case
• Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equations
• Multiple normalized solutions for quasi-linear Schrödinger equations
• Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrodinger Equation
• Multiple solutions to the nonlinear Schrödinger equation with a partial confinement
• Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
• Nonradial normalized solutions for a quasilinear Schrödinger equation via dual approach
• Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
• Solitary Wave Dynamics in an External Potential
• Normalized solutions for the fractional NLS with mass supercritical nonlinearity
• Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in \mathbb R²
• On sharp scattering threshold for the mass-energy double critical NLS via double track profile decomposition
• Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
• The global existence issue for the compressible Euler system with Poisson or Helmholtz couplings
• Ground state solutions of a class of (2,q)-Laplacian Schrödinger equations with inhomogeneous nonlinearity
• Positive normalized solutions to nonlinear elliptic systems in \R⁴ with critical Sobolev exponent
• A Note on Asymptotic Behaviors Of Solutions To Quasilinear Elliptic Equations with Hardy Potential
• On a class quasilinear Schrödinger equations in ℝn
• Global Attraction to Solitary Waves in Models Based on the Klein-Gordon Equation
• Single--peaks for a magnetic Schrödinger equation with critic al growth
• A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity
• Nonradial normalized solutions for nonlinear scalar field equations
• Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
• Multi-speed solitary wave solutions for nonlinear Schrödinger systems
• Solitary wave dynamics in time-dependent potentials
• High-speed excited multi-solitons in nonlinear Schrödinger equations
• An Overview on the Standing Waves of Nonlinear Schrödinger and Dirac Equations on Metric Graphs with Localized Nonlinearity