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.