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On nonlinear Schrödinger equations. (English) Zbl 0632.35038

The nonlinear Schrödinger equation iu t =-Δu+F(u) 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.

Reviewer: L.Brüll

MSC:
35L60Nonlinear first-order hyperbolic equations
35A05General existence and uniqueness theorems (PDE) (MSC2000)
35A07Local existence and uniqueness theorems (PDE) (MSC2000)
35B65Smoothness and regularity of solutions of PDE
35B30Dependence of solutions of PDE on initial and boundary data, parameters