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 a min-max procedure for the existence of a positive solution for certain scalar field equations in ${\bbfR}\sp N$. (English) Zbl 0731.35036
The problem of the existence of positive solutions $u\in H\sp 1({\bbfR}\sp n)$ of the semilinear elliptic equation $$-\Delta u+u- q(x)\vert u\vert\sp{p-1}u=0 $$ is considered. Under suitable conditions on p,n and $q(x)\in L\sp{\infty}({\bbfR}\sp n)$ a min-max procedure for the corresponding variational functional J which is based on topological methods shows the existence of at least one positive solution.

35J65Nonlinear boundary value problems for linear elliptic equations
47H11Degree theory (nonlinear operators)
58E05Abstract critical point theory
Full Text: DOI EuDML