Geodesic
On the oscillation of certain difference equations
Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 421-430

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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 $\mu\geq0$.
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 $\mu\geq0$.
DOI : 10.21136/MB.2000.126277
Classification : 39A10, 39A11, 39A12
Keywords: oscillation; delay difference equations; forced equations 
Grace, S. R.; El-Morshedy, H. A. On the oscillation of certain difference equations. Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 421-430. doi: 10.21136/MB.2000.126277
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