Uniqueness of positive solutions of Δu−u+up=0 in Rn

1989/09/01 by Man Kam Kwong · 75 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · doi:10.1007/bf00251502

Citations

• Nonlinear scalar field equations, II existence of infinitely many solutions
• Nonlinear scalar field equations, I existence of a ground state

Cited by

• Normalized ground states for the NLS equation with combined nonlinearities
• The Schrödinger–Poisson equation under the effect of a nonlinear local term
• On spinor elliptic system: Uniqueness and symmetry breaking
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS
• On Threshold Solutions of equivariant Chern-Simons-Schrödinger Equation
• Band-edge solitons, Nonlinear Schrodinger / Gross-Pitaevskii Equations\n and Effective Media
• Threshold solutions in the focusing 3D cubic NLS equation outside a\n strictly convex obstacle
• Cluster solutions for the Schrodinger-Poisson-Slater problem around a local minimum of the potential
• On supercritical nonlinear Schrödinger equations with ellipse-shaped potentials
• Ground states for a system of nonlinear Schrodinger equations with three waves interaction
• Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations
• On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations
• On the blowup for the L²-critical focusing nonlinear Schrödinger equation in higher dimensions below the energy class
• Existence of standing waves for the complex Ginzburg-Landau equation
• Construction of solitary wave solution of the nonlinear focusing schrödinger equation outside a strictly convex obstacle for the L²-supercritical case
• Normalized solutions for nonlinear Schrödinger systems with special mass-mixed terms: The linear couple case
• On the L²-critical nonlinear Schrödinger Equation with a nonlinear damping
• Nondegeneracy of nonradial sign-changing solutions to the nonlinear Schrödinger equations
• Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential
• Infinitely many positive solutions for nonlinear fractional Schrödinger equations
• Existence and asymptotic behavior of normalized solution for Schrödinger equation with Hartree nonlinearities
• A Critical Centre-Stable Manifold for Schroedinger's Equation in R³
• Normalized ground states for semilinear elliptic systems with critical and subcritical nonlinearities
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• Scattering for the cubic Klein--Gordon equation in two space dimensions
• Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
• Quantitative Properties on the Steady States to A Schrödinger-Poisson-Slater System
• Sharp interaction estimates and their application: existence of normalized ground states to coupled Schrödinger systems with potentials
• The double-power nonlinear Schr "odinger equation and its\n generalizations: uniqueness, non-degeneracy and applications
• Stationary solutions of the Schrödinger-Newton model - An ODE approach
• Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity
• Semi-classical states for the Nonlinear Schr "odinger Equation on saddle\n points of the potential via variational methods
• Existence and Asymptotic Behavior of Ground States for Rotating Bose-Einstein Condensates
• Radial Symmetry and Monotonicity Results for an Integral Equation
• Positive solutions for autonomous and non-autonomous nonlinear critical\n elliptic problems in exterior domains
• Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d≥3 equations
• Threshold solutions for the focusing 3d cubic Schroedinger equation
• Numerical verification of a gap condition for linearized NLS
• Modulational stability of ground states to nonlinear Kirchhoff equations
• Self-similar extinction for a diffusive Hamilton-Jacobi equation with critical absorption
• On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d≥ 2
• Existence of Strong Solution for the Complexified Non-linear Poisson Boltzmann Equation
• Scattering for the focusing energy-subcritical NLS
• Mass Concentration and Local Uniqueness of Ground States for L²-subcritical Nonlinear Schrödinger Equations
• Normalized solutions and mass concentration for supercritical nonlinear Schrödinger equations
• Regularity of almost periodic modulo scaling solutions for mass-critical NLS and applications
• Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth
• Multiple normalized standing-waves solutions to the scalar non-linear\n Klein-Gordon equation with two competing powers
• On sharp scattering threshold for the mass-energy double critical NLS via double track profile decomposition
• Asymptotic stability of N-soliton states of NLS
• Ground states for 3D dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses
• Remarks on Nondegeneracy of Ground States for Quasilinear Schrödinger Equations
• A Liouville Theorem for a Class of Fractional Systems in ℝⁿ₊
• Qualitative properties of positive solutions for mixed integro-differential equations
• Dispersive estimates for Schroedinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: II
• Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation
• Asymptotic K-soliton-like Solutions of the Zakharov-Kuznetsov type equations
• Existence of positive solution for a class of nonlocal elliptic problems in the half space with a hole
• Strongly interacting blow up bubbles for the mass critical NLS
• Stationary focusing Mean Field Games
• Théorèmes de de Finetti, limites de champ moyen et condensation de Bose-Einstein
• The global bifurcation picture for ground states in nonlinear\n Schrodinger equations
• On smoothness and uniqueness of multi-solitons of the non-linear\n Schr "odinger equations
• Spectral Theory and Nonlinear PDE: a Survey
• Orbital stability of solitary waves for the generalized Choquard model
• On Elliptic Equations and Systems involving critical Hardy-Sobolev exponents (non-limit case)
• On the second minimax level for the scalar field equation
• Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential
• Positive normalized solutions to nonlinear elliptic systems in \R⁴ with critical Sobolev exponent
• A Critical Centre-Stable Manifold for the Cubic Focusing Schroedinger Equation in Three Dimensions
• Uniqueness and orbital stability of standing waves for the nonlinear Schrodinger equation with a partial confinement
• Multi-soliton dynamics in the nonlinear Schrödinger equation
• The Toda system and multiple-end solutions of autonomous planar elliptic problems
• Bounds states of the Schrödinger-Newton model in low dimensions
• On the vortices for the nonlinear Schrödinger equation in higher dimensions. [europepmc]