# Article

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Keywords:
perturbed quasilinear difference equation; oscillatory solution
Summary:
This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form $\Delta (a_{n-1}| \Delta y_{n-1}|^{\alpha -1} \Delta y_{n-1})+ F(n, y_n)= G(n, y_n, \Delta y_n), \quad n\in N(n_0) \qquad \mathrm {(E)}$ where $\alpha >0$. Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.
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