Nonlinear Schrodinger equation with singular potential and initial data

We consider a nonlinear Schrodinger equation with singular potential and initial data when the nonlinear term is an L-loc(infinity)-function which does not satisfy the Lipschitz condition. To avoid non-Lipshitz nonlinearity we use the cut-off method of regularization and as a framework for existence-uniqueness theorems we employ Colombeau vector space G(C1, W2,2) ([0, T), R-n), n <= 3. As an example we prove the existence-uniqueness result for nonlinear mapping f(u) = vertical bar u vertical bar(p-1)u, p >= 1, in the space G(C1, W2,2) ([0, T), R-n), n <= 3. (c) 2005 Published by Elsevier Ltd.