S. R. Grace, Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12000, Egypt; H. A. El-Morshedy, Department of Mathematics, Damietta Faculty of Science, New Damietta 34517, Egypt
Abstract: In this paper we study the oscillation of the difference equations of the form
\Delta^2x_n+p_n\Delta x_n+f(n, x_{n-g}, \Delta x_{n-h})=0,
in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation
\Delta^2x_n+p_n\Delta x_n+q_n|x_{n-g}|^{\lambda}|\Delta x_{n-h}|^{\mu}\sgn x_{n-g}=0,
where $\lambda$ and $\mu$ are real constants, $\lambda>0$ and $\mu\geq0$.
Keywords: oscillation, delay difference equations, forced equations
Classification (MSC 1991): 39A10, 39A12
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