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On nonlinear Schrödinger equations. (English) Zbl 0632.35038
The nonlinear Schrödinger equation \(iu_ t=-\Delta u+F(u)\) 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:
35L60 First-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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References:
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