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Oscillation and comparison theorems for half-linear second-order difference equations. (English) Zbl 0983.39006
Authors’ abstract: The authors consider second-order difference equations of the type $$\Delta\bigl((\Delta y_n)^\alpha \bigr)+ q_ny^\alpha_{ \sigma (n)}=0, \tag E$$ where $\alpha>0$ is the ratio of odd positive integers, $\{q_n\}$ is a positive sequence, and $\{\sigma(n)\}$ is a positive increasing sequence of integers with $\sigma(n) \to\infty$ as $n\to\infty$. They give some oscillation and comparison results for equation (E).

39A11Stability of difference equations (MSC2000)
Full Text: DOI
[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. S.: Hille-wintner type comparison theorems for nonlinear difference equations. Funkcial. ekvac. 37, 531-535 (1994) · Zbl 0820.39003
[4] Chen, S. S.; Zhang, B. G.: Monotone solutions of a class of nonlinear difference equations. Computers math. Applic. 28, No. 1--3, 71-79 (1994)
[5] Li, H. J.; Yeh, C. C.: Existence of positive nondecreasing solutions of nonlinear difference equations. Nonlinear anal. 22, 1271-1284 (1994) · Zbl 0805.39004
[6] Thandapani, E.; Arul, R.: Oscillation and nonoscillation theorems for a class of second order quasilinear difference equations. Z. anal. Anwendungen 16, 749-759 (1997) · Zbl 0883.39007
[7] Thandapani, E.; Graef, J. R.; Spikes, P. W.: On the oscillation of solutions of second order quasilinear difference equations. Nonlinear world 3, 545-565 (1996) · Zbl 0897.39002
[8] Thandapani, E.; Manuel, M. M. S.; Agarwal, R. P.: Oscillation and nonoscillation theorems for second order quasilinear difference equations. Facta univ. Ser. math. Inform. 11, 49-65 (1996) · Zbl 1014.39004
[9] E. Thandapani and L. Ramuppillai, Oscillation and nonoscillation of quasilinear difference equations of the second order, Glasnik Math. (to appear). · Zbl 0923.39007
[10] Thandapani, E.; Ravi, K.: Bounded and monotone properties of solutions of second-order quasilinear forced difference equations. Computers math. Applic. 38, No. 2, 113-121 (1999) · Zbl 0936.39003
[11] Thandapani, E.; Ravi, K.: Oscillation of second-order half-linear difference equations. Appl. math. Lett. 13, No. 2, 43-49 (2000) · Zbl 0977.39003
[12] Wong, P. J. Y.; Agarwal, R. P.: Oscillations and nonoscillations of half-linear difference equations generated by deviating arguments. Computers math. Applic. 36, No. 10--12, 11-26 (1998) · Zbl 0933.39025
[13] Onose, H.: A comparison theorem and the forced oscillation. Bull. austral. Math. soc. 13, 13-19 (1975) · Zbl 0307.34034
[14] Kusano, T.; Naito, M.: Comparison theorems for functional differential equations with deviating arguments. J. math. Soc. Japan 33, 509-532 (1981) · Zbl 0494.34049
[15] Mahfoud, W. E.: Comparison theorems for delay differential equations. Pacific J. Math. 83, 187-197 (1979) · Zbl 0441.34053