Oscillatory and asymptotic behaviour of fourth order nonlinear neutral delay difference equations. (English) Zbl 1004.39005

Thandapani, E.; Arockiasamy, I. M.

Indian J. Pure Appl. Math. 32, No. 1, 109-123 (2001).

The author considers the following nonlinear neutral delay difference equation \[ \Delta^2[r_n\Delta(y_n+p_ny_{n-k})]+f(n, y_{\sigma(n)})=0, \] where \(r_n>0, p_n>0\) and \(\{\sigma(n)\}\) is an increasing sequence of integers. Necessary and sufficient conditions are obtained for the existence of non-oscillatory solutions with a special asymptotic behaviour; also, sufficient conditions are obtained for all solutions to be oscillatory.

Reviewer: Xianhua Tang (Changsha)

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

asymptotic behaviour; oscillatory solution; nonlinear neutral delay difference equation; non-oscillatory solutions