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)
Remarks on oscillation and nonoscillation for second-order linear difference equations. (English) Zbl 1161.39014
In this remark, the authors consider the second-order linear difference equation $$ \Delta^2x_{n-1}+p_nx_n=0,\quad n\geq n^0, $$ where $\{p_n\}^{\infty}_{n=1}$ is a real sequence with $p_n\geq 0$ for $ n\geq n^0$. The main contribution is two-fold. One is to show that the main results of an earlier work by {\it W. T. Li} and {\it S. S. Cheng} [ibid. 16, No. 2, 161--163 (2003; Zbl 1052.39009)] are incorrect. The other is to obtain a generalized criterium about the oscillation and nonoscillation of the equation.

39A11Stability of difference equations (MSC2000)
39A10Additive difference equations
Full Text: DOI
[1] Agarwal, R. P.: Difference equations and inequalities. (2000) · Zbl 0952.39001
[2] Cheng, S. S.; Yan, T. C.; Li, H. J.: Oscillation criteria for second order difference equation. Funkcial. ekvac. 34, 223-239 (1991) · Zbl 0773.39001
[3] Li, W. T.; Cheng, S. S.: Remarks on two recent oscillation theorems for second-order linear difference equations. Appl. math. Lett. 16, 161-163 (2003) · Zbl 1052.39009
[4] Zhang, B. G.; Cheng, S. S.: Oscillation criteria and comparison theorems for delay difference equations. Fasc. math. 25, 13-32 (1995) · Zbl 0830.39005
[5] Zhang, B. G.; Zhou, Yong: Oscillation and nonoscillation of second order linear difference equation. Comput. math. Appl. 39, No. 1--2, 1-7 (2000) · Zbl 0973.39007