Ground states of a coupled pseudo-relativistic Hartree system: existence and concentration behavior
arXiv:2407.15495 · doi:10.1016/j.jde.2025.02.019
Abstract
This paper is concerned with the ground states of a coupled pseudo-relativistic Hartree system in with trapping potentials, where the intraspecies and the interspecies interaction are both attractive. By investigating an associated constraint minimization problem, the existence and non-existence of ground states are classified completely. Under certain conditions on the trapping potentials, we present a precise analysis on the concentration behavior of the minimizers as the coupling coefficient goes to a critical value, where the minimizers blow up and the maximum point sequence concentrates at a global minima of the associated trapping potentials. We also identify an optimal blowing up rate under polynomial potentials by establishing some delicate estimates of energy functionals.
arXiv comment34 pages
References in corpus (13)
- Ground state solutions for nonlinear fractional Schrödinger equations in
- Local behavior of fractional -minimizers
- On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions
- Boson Stars as Solitary Waves
- Uniqueness of Ground States for Pseudo-Relativistic Hartree Equations
- Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
- On Singularity formation for the L^2-critical Boson star equation
- Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation
- Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions
- Existence and mass concentration of pseudo-relativistic Hartree equation
- Blow-up behavior of ground states for a nonlinear Schrödinger system with attractive and repulsive interactions
- On Blow-up Profile of Ground States of Boson Stars with External Potential
- A constrained minimization problem related to two coupled pseudo-relativistic Hartree equations