**S. H. Saker**

## Oscillation Theorems of Nonlinear Difference
Equations

of Second Order

**abstract:**

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.