zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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

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