Persistence of the Thomas-Fermi approximation for ground states of the Gross-Pitaevskii equation supported by the nonlinear confinement

We justify the Thomas-Fermi approximation for the stationary Gross-Pitaevskii equation with the repulsive nonlinear confinement, which was recently introduced in physics literature. The method is based on the resolvent estimates and the fixed-point iterations. The results cover the case of the algebraically growing nonlinear confinement.