Threshold behavior and uniqueness of ground states for mass critical inhomogeneous Schrödinger equations

DOI10.1063/1.5008924zbMath1383.35208OpenAlexW2784829633MaRDI QIDQ3134096

Lu Lu, Yinbin Deng, Yujin Guo

Publication date: 8 February 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5008924

zbMATH Keywords

Gross-Pitaevskii energymass critical Schrödinger equations

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Quantum dots, waveguides, ratchets, etc. (81Q37) Quantum waveguides, quantum wires (82D77)

Related Items (8)

Concentration behavior of ground states for \( L^2\)-critical Schrödinger equation with a spatially decaying nonlinearity ⋮ Vortex states of Bose-Einstein condensates with attractive interactions ⋮ Existence and local uniqueness of normalized peak solutions for a Schrödinger-Newton system ⋮ Non-existence of multi-peak solutions to the Schrödinger-Newton system with \(L^2\)-constraint ⋮ Minimizers of \(L^2\)-subcritical variational problems with spatially decaying nonlinearities in bounded domains ⋮ Minimizers of \(L^2\)-subcritical inhomogeneous variational problems with a spatially decaying nonlinearity ⋮ \(L^2\) normalized solutions for nonlinear Schrödinger systems in \(\mathbb{R}^3\) ⋮ Existence and uniqueness of ground states for attractive Bose–Einstein condensates in box-shaped traps

Cites Work

• Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
• On the collapse and concentration of Bose-Einstein condensates with inhomogeneous attractive interactions
• Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions
• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Self-dual gauge field vortices. An analytical approach
• On the bound states of the nonlinear Schrödinger equation with a linear potential
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• Nodal standing waves for a gauged nonlinear Schrödinger equation in \(\mathbb{R}^2\)
• On concentration of positive bound states of nonlinear Schrödinger equations
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation
• On the mass concentration for Bose-Einstein condensates with attractive interactions
• Radial symmetry of positive solutions of nonlinear elliptic equations in Rⁿ
• Uniqueness of standing waves for nonlinear Schrödinger equations
• Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross–Pitaevskii Equations
• On the shape of least‐energy solutions to a semilinear Neumann problem
• Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials
• Variational Methods
• Stability of attractive Bose-Einstein condensates
• A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
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