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)
Oscillation theorem for second-order difference equations. (English) Zbl 1157.39004

The authors study the following second-order difference equation,

Δ(r n-1 Δx n-1 )+p n x n γ =0,n=1,2,...,(*)

where Δx n =x n+1 -x n , γ is the quotient of odd positive integers and p n , r n (0,) for n=1, 2, ... with p n not eventually zero. The obtained results include sufficient condition for the existence of bounded nonoscillatory solution to (*) and respective sufficient and necessary conditions for every bounded solution of (*) to oscillate for the cases where γ>1, γ=1, and γ(0,1). These results not only generalize those for the case where r n 1 but also improve some of them.

39A11Stability of difference equations (MSC2000)
39A10Additive difference equations