zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Stationary patterns of strongly coupled prey–predator models. (English) Zbl 1160.35325

The author considers the strongly coupled system

-div(K(u)u)=G(u)inΩ,u n=0onΩ·(1)

The author establishes a priori upper and lower bounds for positive solutions of (1), and studies the non-existence of nonconstant positive solutions. Moreover the author considers the bifurcation and the global existence with respect to diffusion terms of nonconstant positive solutions. The analysis of the author shows that the cross-diffusions may be source for the stationary patterns.

MSC:
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J55Systems of elliptic equations, boundary value problems (MSC2000)
92D25Population dynamics (general)