Oscillation of nonlinear neutral delay difference equations of fourth order

Abstract

This paper focuses on the study of the oscillatory behavior of fourth-order nonlinear neutral delay difference equations. The authors use mathematical techniques, such as the Riccati substitution and comparison technique, to explore the regularity and existence properties of the solutions to these equations. The authors present a new form of the equation: Delta(a(m)(Delta(3)z(m))(p1-1))+p(m)w(p2-1)(sigma(m))=0, where z(m)=w(m)+q(m)w(m-tau) with the following conditions: Sigma(infinity)(s=m0) 1/a(1/p(1)-1(s))=infinity. The equation represents a system where the state of the system at any given time depends on its current time and past values. The authors demonstrate new insights into the oscillatory behavior of these equations and the conditions required for the solutions to be well-behaved. They also provide a numerical example to support their findings.