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)
Multiparameter local bifurcation based on the linear part. (English) Zbl 0668.47042
We give a result in multiparameter local bifurcation theory. This result is a generalization of the Hopf bifurcation theorem and of a previous result by {\it J. K. Hale} [Nonlinear Anal., Theory Methods Appl. 2, 491- 497 (1978; Zbl 0383.34050)]. Our result can be applied to Fredholm operators with arbitrary index.

47J05Equations involving nonlinear operators (general)
47A53(Semi-) Fredholm operators; index theories
Full Text: DOI
[1] Chow, S. N.; Hale, J. K.: Methods of bifurcation theory. (1982) · Zbl 0487.47039
[2] Crandall, M. G.; Rabinowitz, P. H.: Bifurcation from simple eigenvalues. J. funct. Anal. 8, 321-340 (1971) · Zbl 0219.46015
[3] Crandall, M. G.; Rabinowitz, P. H.: The Hopf bifurcation theorem. Tech. sum. Rep. MRC, no. 1604 (1976) · Zbl 0385.34020
[4] Hale, J. K.: Bifurcation from simple eigenvalues for several parameter families. Nonlinear anal. TMA 2, 491-497 (1978) · Zbl 0383.34050
[5] López-Gómez, J.: Hopf bifurcation at multiple eigenvalues with zero eigenvalue. Proc. roy. Soc. Edinburgh ser. A 101, 335-352 (1985) · Zbl 0582.34053