Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

E. Thandapani and L. Ramuppillai

Address. Department of Mathematics, Madras University P.\,G.\,Centre, Salem-636 011, Tamil Nadu, INDIA


Abstract. This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form $$ \Delta (a_{n-1}| \Delta y_{n-1}|^{\alpha-1} \Delta y_{n-1})+ F(n, y_n)= G(n, y_n, \Delta y_n), \quad n\in N(n_0) \tag{E} $$ 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.

AMSclassification. 39A10

Keywords. Perturbed quasilinear difference equation, oscillatory solution