Qualitative inspection fourth order non linear difference equations

Abstract

In this paper, the authors obtained some new sufficient conditions for the oscillation of all solutions of the fourth order nonlinear difference equation of the form ∆3 (an ∆xn) - pn ∆xn + qn f (xn+1) = 0 n = 0,1,2, …, where an, pn, qn positive sequences. The established results extend, unify and improve some of the results reported in the literature. Examples are provided to illustrate the main result.