Oscillation and nonoscillation of quasilinear difference equations of second order

In this paper the authors establish conditions for the oscillatory and nonoscillatory behavior of solutions of second order quasilinear difference equations Δ(an -1 |Δyn -1|α-1 Δyn -1) + qn f(yn) = 0 and Δ(an -1 |Δyn -1|α-1 Δyn -1) + qn f(yn -λ) = 0 when {qn}, {an} and the function f satisfy different type of conditions. Examples are inserted to illustrate our results

Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

summary:In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma$ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma <1)$

Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

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