Oscillation of 2nd-order Nonlinear Noncanonical Difference Equations with Deviating Argument

The purpose of this paper is to establish some new criteria for the oscillation of the second-order nonlinear noncanonical difference equations of the form \ \Delta \left( a\left( n\right) \Delta x\left( n\right) \right) +q(n)x^{\beta }\left( g(n)\right) =0,\text{ \ \ }n\geq n_{0} \] under the assumption \ \sum_{s=n}^{\infty }\frac{1}{a\left( s\right) }<\infty \text{.} \] Corresponding difference equations of both retarded and advanced type are studied. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.