ENERGY METHODS FOR HARTREE TYPE EQUATIONS WITH INVERSE-SQUARE POTENTIALS

Nonlinear Schrodinger equations with nonlocal nonlinearities described by integral operators are considered. This generalizes usual Hartree type equations (HE)(0). We construct weak solutions to (HE), a a not equal 0, even if the kernel is of non-convolution type. The advantage of our methods is the applicability to the problem with strongly singular potential a vertical bar x vertical bar(-2) as a term in the linear part and with critical nonlinearity.