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.
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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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/

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