Nonlinear Schrödinger equation with singular potential and initial data

We consider a nonlinear Schrödinger equation with singular potential and initial data when the nonlinear term is an Lloc∞-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 GC1,W2,2GC1,W2,2([0,T),Rn),([0,T),Rn),n⩽3.n⩽3. As an example we prove the existence–uniqueness result for nonlinear mapping f(u)=|u|p-1u,f(u)=|u|p-1u,p⩾1,p⩾1, in the space GC1,W2,2([0,T),Rn),GC1,W2,2([0,T),Rn),n⩽3.n⩽3.