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)
Sharp conditions for nonoscillation of functional equations. (English) Zbl 1007.39018

The authors consider a couple of functional equations related to the realm of second-order linear difference equations with continuous arguments, for which previous work in the last ten years has concentrated mainly on necessary and sufficient conditions entailing the oscillatory nature of all solutions, and little attention has been given to the nonoscillatory ones.

The paper is devoted to consider sharp conditions guaranteeing the existence of nonoscillatory solutions for these equations. In one of the two cases dealt with, the authors improve and generalize the incipient known results using arguments relying on a couple of ground results of functional analysis. For the other case the study is reduced to the detailed consideration of several first-order nonlinear functional equations.

MSC:
39B22Functional equations for real functions
39A11Stability of difference equations (MSC2000)