S. H. Saker

Oscillation Theorems of Nonlinear Difference Equations
of Second Order

Using the Riccati transformation techniques, we establish some new oscillation criteria for the second-order nonlinear difference equation
\Delta ^{2}x_{n}+F(n,x_{n},\Delta x_{n})=0\quad \text{for}\quad
n\geq n_{0}.
Some comparison between our theorems and the previously known results in special cases are indicated. Some examples are given to illustrate the relevance of our results.