Oscillation Criteria for Third-Order Nonlinear Functional Difference Equations with Damping

Abstract

In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

Oscillation of third-order delay difference equations with negative damping term

“…In (1.2) and (1.3), the authors assumed the coefficient sequence of the damping term is positive, and therefore, in this paper, we investigate the oscillatory and asymptotic behavior of solutions of (1.1) by assuming the coefficient of the damping term is negative. Thus the results obtained in this paper are new and complement those in [5], [6], [10], [12], [13].…”

“…∆(a n ∆(b n ∆y n )) + p n ∆y n+1 + q n f (y n− ) = 0, n ≥ n 0 , and established some new sufficient conditions for the oscillation and asymptotic behavior of solutions of (1.2). Very recently, in [6], the authors discussed the oscillatory and asymptotic behavior of solutions of the equation…”

Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments

“…Bohner et al [6,7] and Džurina and Kotorová [10] studied the oscillatory behavior of a third-order delay differential equation with damping…”

Oscillation of nonlinear third-order difference equations with mixed neutral terms

“…Oscillation of solutions for third-order difference equations has received comparably little attention, although such equations are of importance in many fields of science such as economics, physics, mathematical biology, and other areas of mathematics [3,4,6,7,10,11,13,14,24,27,31,32,[35][36][37]. It is worth to mention that third-order difference equations may have totally different behavior from corresponding third-order differential equations; see the explicit example in [9].…”