# 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)
Oscillation and non-oscillation for second-order linear difference equations. (English) Zbl 1103.39300
Oscillation and non-oscillation theorems are proved for the second-order linear difference equation $$\Delta^2x_{n-1} + p_{n}x_{n} = 0$$ when $(p_{n})$ is a real nonnegative sequence. The main results are discrete analogues of some theorems of Wong for second order ordinary differential equations and generalize earlier results of Zhang and Zhou.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
##### Keywords:
oscillation; non-oscillation; difference equation
Full Text:
##### References:
 [1] Agarwal, R. P.: Difference equations and inequalities. (1992) · Zbl 0925.39001 [2] Agarwal, R. P.; Wong, P. J. Y.: Advanced topics in difference equations. (1997) · Zbl 0878.39001 [3] Chen, S. Z.; Erbe, L. H.: Riccati techniques and discrete oscillations. J. math. Anal. appl. 142, 468-487 (1989) · Zbl 0686.39001 [4] Došlý, O.; Řehák, P.: Nonoscillation criteria for half-linear second order difference equations. Comput. math. Appl. 42, 453-464 (2001) · Zbl 1006.39012 [5] Erbe, L. H.: Oscillation of second-order linear difference equations. Chin. J. Math. 16, 239-252 (1998) · Zbl 0692.39001 [6] Jiang, J.; Li, X.: Oscillation criteria for second-order linear difference equations. Appl. math. Comput. 145, 591-691 (2003) · Zbl 1036.39009 [7] Liu, B.; Cheng, S. S.: Positive solutions of second order nonlinear difference equations. J. math. Anal. appl. 198, 482-493 (1996) · Zbl 0872.39004 [8] Zhang, B. G.; Zhou, Y.: Oscillation and non-oscillation for second-order linear difference equations. Comput. math. Appl. 39, 1-7 (2000) · Zbl 0973.39007 [9] Cheng, S. S.; Patula, W. T.: An existence theorem for a nonlinear difference equation. Nonlinear anal. 20, 193-203 (1993) · Zbl 0774.39001 [10] Cheng, S. S.; Zhang, B. G.: Monotone solutions of a class of nonlinear difference equations. Comput. math. Appl. 28, 71-79 (1994) · Zbl 0805.39005 [11] Cheng, S. S.; Zhang, B. G.: Nonexistence of positive nondecreasing solutions of a nonlinear difference equation. Proceedings of the first international conference on difference equations (1995) · Zbl 0860.39006 [12] Cheng, S. S.: Hille-wintner type comparison theorems for nonlinear difference equations. Funkc. ekv. 37, 531-535 (1994) · Zbl 0820.39003 [13] Huang, C.: Oscillation and nonoscillation for second order linear differential equations. J. math. Anal. appl. 210, 712-723 (1997) · Zbl 0880.34034 [14] Wong, J. S. W.: Remarks on a paper of C. Huang. J. math. Anal. appl. 291, 180-188 (2004) · Zbl 1046.34061