OSCILLATORY BEHAVIOR OF SECOND ORDER NONLINEAR DAMPED NEUTRAL DIFFERENCE EQUATION

Abstract

This paper deals with oscillatory properties of solutions of a class of second order nonlinear damped neutral difference equation of the form:

∆(a_n(∆z_n)^α) + p_n(∆z_n)^α + q_n f(x_{n−l}) = 0, n ≥ n_0. (E)

where z_n = x_n − b_n x_{n−k}. Some new sufficient conditions are obtained which ensure that all solutions of equation (E) are oscillatory. The results presented in this paper extend and improve some of the related results reported in the literature. Examples are provided to illustrate the importance of the main results.