Nonoscillation criteria for half-linear second-order difference equations (Q1600392)

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.