The nonlinear Schrödinger equation is considered.
The author investigates questions concerning the local and global existence, uniqueness, continuous dependence on the initial value and regularity of the solution of the corresponding Cauchy problem.
The introduction contains a clear and condensed representation of the theorems. Therefore, it gives a good survey on recent results for the initial value problem. As the author remarks, not all results are new. However, all theorems are proved without using growth conditions of F(x) for small x.