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| Oscillation of 2nd-order Nonlinear Noncanonical Difference Equations with Deviating Argument |
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| KeyWord:Nonlinear difference equation Retarded Advanced Noncanonical Oscillation |
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| Abstract: |
| 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. |
