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

摘要

A class of nonlinear Schrödinger 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 ℝ N and in bounded domains. Supported by Italy MIUR, national project “Variational Methods and Nonlinear Differential Equations”.