Asymptotic Properties Of Third Order Nonlinear Difference Equations With Mixed Arguments

Abstract

In this paper, we offer sufficient conditions for property (B) and/or
the oscillation of third order nonlinear difference equation with
mixed arguments of the form
?( a_n( ?²  x_n)^?) = q_nf(x_n-l) = p_nh(x_n+m),n ? N_o

where {a_n}, {p_n},  {q_n} are nonnegative real sequences, 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 and oscillation are resulted from the oscillation of a set of first order difference equations. Both cases

 are considered. Some examples are provided to
illustrate the main results.