Properties of ground states of attractive Gross–Pitaevskii equations with multi-well potentials

DOI10.1088/1361-6544/aa99a8zbMath1396.35018arXiv1502.01839OpenAlexW2963779751MaRDI QIDQ4635061

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Publication date: 13 April 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.01839

zbMATH Keywords

Gross-Pitaevskii equationground statesconstrained variational problem

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Uniqueness of positive radial solutions of \(\Delta u+f(u)=0\) in \({\mathbb{R}}^ n\)
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation
• Standing waves with a critical frequency for nonlinear Schrödinger equations
• On concentration of positive bound states of nonlinear Schrödinger equations
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations
• 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
• On nonlinear Schrödinger equations with totally degenerate potentials
• Symmetry breaking regime in the nonlinear Hartree equation
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems
• Blow-up profile of Bose-Einstein condensate with singular potentials

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