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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.

##### MSC:
 39A11 Stability of difference equations (MSC2000)
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##### References:
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