On the existence of ground state solutions to nonlinear Schoedinger equations with multisingular inverse-square anisotropic potentials

Abstract

A class of nonlinear Schroedinger equations with critical power-nonlinearities and potentials exhibiting multiple anisotropic inverse square singularities is investigated. Conditions on strength, location, and orientation of singularities are given for the minimum of the associated Rayleigh quotient to be achieved, both in the whole $\R^N$ and in bounded domains.