Positive solutions of the Gross–Pitaevskii equation for energy critical and supercritical nonlinearities

DOI10.1088/1361-6544/acd90azbMath1518.35390arXiv2207.10145MaRDI QIDQ6100656

Wei, Juncheng, Yuanze Wu, Dmitry E. Pelinovsky

Publication date: 22 June 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.10145

zbMATH Keywords

positive solutionsasymptotic behaviourGross-Pitaevskii equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and uniqueness of singular solution to stationary Schrödinger equation with supercritical nonlinearity
• On the Brezis-Nirenberg problem in a ball.
• Symmetry of solutions to variational problems for nonlinear elliptic equations via reflection methods
• Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Best constant in Sobolev inequality
• Self-similar solutions of the pseudo-conformally invariant nonlinear Schrödinger equation
• On some conjectures proposed by Haïm Brezis.
• Elliptic equations with critical Sobolev exponents in dimension 3
• The Brezis-Nirenberg problem near criticality in dimension 3
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Minimax theorems
• Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential
• Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions \(n \geq 7\)
• Energy asymptotics in the Brezis-Nirenberg problem: the higher-dimensional case
• Morse index for the ground state in the energy supercritical Gross-Pitaevskii equation
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Solitary waves and dynamics for subcritical perturbations of energy critical NLS
• A generalized Pohožaev identity and uniqueness of positive radial solutions of \(\Delta u+g(r)u+h(r)u^p=0\)
• Tower of bubbles for almost critical problems in general domains
• Energy asymptotics in the three-dimensional Brezis-Nirenberg problem
• An Introduction to Special Functions
• Radial solutions with prescribed numbers of zeros for the nonlinear Schrödinger equation with harmonic potential
• Global solution branch and Morse index estimates of a semilinear elliptic equation with super-critical exponent
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Positive solutions of elliptic equations involving supercritical growth
• Multispike solutions for a nonlinear elliptic problem involving critical Sobolev exponent
• DOUBLE BLOW-UP SOLUTIONS FOR A BREZIS–NIRENBERG TYPE PROBLEM
• Collapses of Wavefunctions in Multi-Dimensional Coupled Nonlinear Schrödinger Equations under Harmonic Potentials
• Sign-changing blowing-up solutions for the Brezis-Nirenberg problem in dimensions four and five
• The number of positive solutions to the Brezis-Nirenberg problem
• A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions ^*
• Sign-changing tower of bubbles for the Brezis–Nirenberg problem
• Stability and instability of standing waves for the nonlinear Schrödinger equation with harmonic potential
• From best constants to critical functions

This page was built for publication: Positive solutions of the Gross–Pitaevskii equation for energy critical and supercritical nonlinearities