Asymptotic Behavior Of Third Order Nonlinear Difference Equations With Mixed Arguments

Abstract

In this paper, we established criteria for asymptotic properties of nonlinear dierence equation with mixed arguments of the form

? ²(aⁿ(? x_n)^a) + q_nf(x_n-l) + p_nh(x_n+m) = 0,    n ? N ₀
where {a_n},  {p_n} and {q_n} are nonnegative real sequences,  a is a ratio of odd positive integer, and l and m are positive integers. We duduce the properties of studied equation by establishing new comparison theorem, so that some asymptotic properties of nonoscillatory solutions are resulted from the oscillation of a set of first order difference equations. Some examples are provided to illustrate the main results.