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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:
39A11Stability of difference equations (MSC2000)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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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