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Oscillation of fourth order nonlinear neutral difference equations-II

Authors:

A. K. Tripathy

Affiliation:

(1) Department of Mathematics, Kakatiya Institute of Technology & Science, Warangal, 506015, India

Abstract:

Oscillatory and asymptotic behaviour of solutions of a class of fourth order nonlinear neutral difference equations of the form

$$
Delta ^2 (r(n)Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = 0
$$

and

$$
(E) Delta ^2 (r(n)Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = f(n)
$$

are studied under the assumption $sumlimits_{n = 0}^infty {tfrac{n} {{r(n)}}}$ < ∞, for different ranges of p(n). Sufficient conditions are obtained for the existence of positive bounded solutions of (E).

Keywords:

oscillation non-oscillation neutral difference equations existence of positive solutions asymptotic behaviour

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