Geodesic
Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations
Archivum mathematicum, Tome 34 (1998) no. 4, pp. 455-466.

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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.
Classification : 39A11
Keywords: perturbed quasilinear difference equation; oscillatory solution 
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     author = {Thandapani, E. and Ramuppillai, L.},
     title = {Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations},
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     pages = {455--466},
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Thandapani, E.; Ramuppillai, L. Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations. Archivum mathematicum, Tome 34 (1998) no. 4, pp. 455-466. http://geodesic.mathdoc.fr/item/ARM_1998__34_4_a4/