ABSTRACT
This chapter presents an overview on some classes of nonlinear Schrodinger equations which contain linear and nonlinear terms of various singular types. It gives a list of specific problems of this type from mathematical physics including some which can only live in the framework of ‘Generalized Functions’. The chapter applies an implicit function theorem of Nash-Moser type for Frechet spaces to prove the local well-posedness for some nonlinear Schrodinger type equation. The existence theory for linear Schrodinger equations with time-dependent potentials developed by Yajima can be extended such that potentials of this singular type are allowed. This extension is achieved by generalizing Strichartz estimates to certain Lorentz spaces.
