Nonlinear scalar field equations, I existence of a ground state

1983/12/01 by H. Berestycki, Henri Berestycki, P. -L. Lions +1 · 59 citations
Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Advanced Mathematical Physics Problems #Cosmology and Gravitation Theories

paper · doi:10.1007/bf00250555

Cited by

• Uniqueness of positive solutions of Δu−u+up=0 in Rn
• Solitons and Scattering for the Cubic–Quintic Nonlinear Schrödinger Equation on ℝ³ R 3
• On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases
• Normalized ground states for the NLS equation with combined nonlinearities
• Nodal standing waves for a gauged nonlinear Schrödinger equation in R 2
• Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
• Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schrödinger equations
• 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
• Static solutions for Choquard equations with Coulomb potential and upper critical growth
• Trace and Hardy-Sobolev type inequalities and applications to a quasilinear elliptic problem in half-space
• Ground state solutions for Hartree type equations driven by superposition operators and Pohozaev Identity
• L²-Supercritical Nonlinear Klein-Gordon System with Quadratic Asymmetric Interaction
• Threshold solutions in the focusing 3D cubic NLS equation outside a\n strictly convex obstacle
• Standing waves of the Anderson-Gross-Pitaevskii equation
• Ground states for a system of nonlinear Schrodinger equations with three waves interaction
• Polyharmonic Nonlinear Scalar Field Equations
• Ground state solutions to the nonlinear Born-Infeld problem
• On the ground state of the nonlinear Schrödinger equation: asymptotic behavior at the endpoint powers
• Normalized solutions of L² supercritical NLS equations in exterior domains with inhomogeneous nonlinearities
• Normalized solutions for the planar Schrödinger-Poisson system with two electrons interaction
• Resolving Sharp Gradients of Unstable Singularities to Machine Precision via Neural Networks
• Normalized solutions for the Sobolev critical Schrödinger equation with trapping potential
• Uniqueness of radial solutions for m-Laplacian equations in low dimensions
• Normalized Solutions for the (2,q)-Laplacian Operator Between Mass-Critical Exponents
• Nonlinear scalar field equations with a critical Hardy potential
• SOLITARY WAVES OF THE NONLINEAR KLEIN-GORDON EQUATION COUPLED WITH THE MAXWELL EQUATIONS
• NLS with mass-subcritical combined nonlinearities: small mass L²-scattering
• Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equations
• Existence and asymptotic behavior of normalized solution for Schrödinger equation with Hartree nonlinearities
• Multiple normalized solutions for quasi-linear Schrödinger equations
• On ground states for the 2D Schrodinger equation with combined nonlinearities and harmonic potential
• A multiplicity result for a semilinear Maxwell type equation
• Existence and multiplicity results for the zero mass Schrödinger-Bopp-Podolsky system with critical growth
• From nonlinear Schrödinger equation to interacting particle system: 1 < p < 2
• Existence and qualitative properties of ground state solutions for the Schrödinger-Bopp-Podolsky system
• Morrey--Sobolev inequalities with power weights on the half-space
• Multi-solitons to focusing mass-supercritical stochastic nonlinear Schrödinger equations
• Ground state solutions for the nonlinear Schrodinger-Maxwell equations with a singular potential
• Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space
• Global bifurcation of localised 2D patterns emerging from spatial heterogeneity
• Multiple solutions to the nonlinear Schrödinger equation with a partial confinement
• Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
• The double-power nonlinear Schr "odinger equation and its\n generalizations: uniqueness, non-degeneracy and applications
• Existence and non-existence of minimizers for a multi-particle model with concave nonlinearity
• Solitary Wave Dynamics in an External Potential
• Ground state and multiple solutions for modified autonomous fourth-order elliptic equations with Berestycki-Lions type conditions
• Multiple nodal solutions to a scalar field equation with double-power nonlinearity and zero mass at infinity
• Biharmonic nonlinear vector field equations in ℝ⁴
• Numerical verification of a gap condition for linearized NLS
• On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in ℝ^N
• Nonlinear curl-curl problems in ℝ³
• Normalized solutions for the fractional NLS with mass supercritical\n nonlinearity
• Scattering for the focusing energy-subcritical NLS
• Normalized solutions for the nonlinear Schrödinger equation with potentials
• Pohozaev manifold constraint for solving nonlinear Schrödinger equations with potentials vanishing at infinity
• Multiplicity of positive solutions for nonlinear field equations in \R^N
• Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in \mathbb R²
• On the vortices for the nonlinear Schrödinger equation in higher dimensions. [europepmc]