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)
Coexistence theorems of steady states for predator-prey interacting systems. (English) Zbl 0655.35021
The author gives necessary and sufficient conditions for the existence of positive solutions to the following system: $$ \Delta u+uM(u,v)=0,\quad d\Delta v+v(g(u)-m(v))=0,\quad (u,v)\vert\sb{\partial \Omega}=(0,0),\quad \Omega \subset {\bbfR}\quad n, $$ where M satisfies the so-called prey growth rate conditions, g and m are increasing functions satisfying $g(0)-m(v)<0$ for v larger than some constant C. The paper includes many well-known systems and results as special cases, and some interesting examples are given.
Reviewer: C.F.Wang

35J60Nonlinear elliptic equations
92D25Population dynamics (general)
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35A05General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI