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Nonoscillation criteria for half-linear second-order difference equations. (English) Zbl 1006.39012
Using the Riccati and variational technique, nonoscillation criteria for the half-linear second-order difference equation of the form $$\Delta (r_{k}\Phi (\Delta x_{k}))+c_{k}\Phi (x_{k+1})=0,\quad r_{k}\neq 0,\qquad \Phi (x):=|x|^{p-2}x,\quad p>1$$ are established. Useful remarks and comments are presented in the last section of the paper.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
[1] P. Řehák, Oscillatory properties of second order half-linear difference equations, Czechoslovak Math. J. (to appear).
[2] Agarwal, R. P.: Difference equations and inequalities. (1992) · Zbl 0925.39001
[3] Kelley, W. G.; Peterson, A.: Difference equations: an introduction with applications. (1991) · Zbl 0733.39001
[4] P. Řehák, Oscillation and nonoscillation criteria for second order linear difference equations, Fasc. Math. (to appear).
[5] Došlý, O.: Methods of oscillation theory of half-linear second order differential equations. Czech math. J. 50, No. 125, 657-671 (2000) · Zbl 1079.34512
[6] Kusano, T.; Naito, Y.: Oscillation and nonoscillation criteria for second order quasilinear differential equations. Acta. math. Hungar. 76, 81-99 (1997) · Zbl 0906.34024
[7] Kusano, T.; Naito, Y.; Ogata, A.: Strong oscillation and nonoscillation of quasilinear differential equations of second order. Diff. equations dyn. Syst. 2, 1-10 (1994) · Zbl 0869.34031
[8] Došlý, O.: Oscillation criteria for half-linear second order differential equations. Hiroshima J. Math. 28, 507-521 (1998) · Zbl 0920.34042
[9] O. Došlý and A. Lomtatidze, Oscillation and nonoscillation criteria for half-linear differential equations, (submitted).