Persistence of the Thomas-Fermi approximation for ground states   supported by the nonlinear confinement
  We justify the Thomas--Fermi approximation for the elliptic problem with the repulsive nonlinear confinement used in the recent physical literature. The method is based on the resolvent estimates and the fixed-point iterations. 
Boris A. Malomed and Dmitry E. Pelinovsky
nlin.PS math.AP