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)
Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems. (English) Zbl 0782.35053
The author proves the existence of solutions to the Dirichlet problem for Au=λf(u), where A=-div(|Du| p-2 ) is the p-Laplacian and λ is a positive parameter. The function f vanishes at 0, and is either strictly increasing and O(u μ ) for some μ<p-1, or has a single positive hump. Results for p<2 rely on a strong maximum principle, as in P. Hess [Commun. Partial Differ. Equations 6, 951-961 (1981; Zbl 0468.35073)] and the reviewer’s paper [Houston J. Math. 16, No. 1, 139-149 (1990; Zbl 0717.47026)]. A few results for p>2, and on the necessity of the assumptions of f are also included.

35P30Nonlinear eigenvalue problems for PD operators; nonlinear spectral theory
35J70Degenerate elliptic equations
47H11Degree theory (nonlinear operators)
35J65Nonlinear boundary value problems for linear elliptic equations