We study ground states of mass critical Schrodinger equations with spatially inhomogeneous nonlinearities in R-2 by analyzing the associated L-2-constraint Gross-Pitaevskii energy functionals. In contrast to the homogeneous case where m(x) equivalent to 1, we prove that both the existence and nonexistence of ground states may occur at the threshold a* depending on the inhomogeneity of m(x). Under some assumptions on m(x) and the external potential V(x), the uniqueness and radial symmetry of ground states are analyzed for almost every a is an element of[0, a*). When there is no ground state at ...
