Abstract
The stability and collective excitation of Bose–Einstein condensates with both two- and three-body interactions in a two-dimensional anharmonic trap (i.e., harmonic plus quartic trap) are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability are discussed in detail. It is found that the anharmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.