Property (A) and Oscillation of Third-Order Differential Equations with Mixed Arguments

Abstract

Abstract. In this paper we o¤er criteria for property (A) and the oscillation of the third-order nonlinear functional di¤erential equation with mixed arguments ½aðtÞ½x 0 ðtÞ g 00 þ qðtÞ f ðx½tðtÞÞ þ pðtÞhðx½sðtÞÞ ¼ 0, where Ð y a À1=g ðsÞds ¼ y. We deduce properties of the studied equations by establishing new comparison theorems so that property (A) and the oscillation are resulted from the oscillation of a set of the first order equations.

Oscillation of Third-Order Differential Equations with Advanced Arguments

“…In this paper, we established some new results concerning the oscillation and convergence of Equation (3). We obtained new relationships that allowed us to overcome the difficulties encountered in the previous literature to attain conditions for the oscillation of the solutions; see [8,12,13]. Furthermore, these relationships can be utilised to derive various oscillation conditions using different techniques, such as the integrated average technique and comparison principles.…”

“…Later, the results of (1) were subsequently extended to include noncanonical forms, see [8,12]. On the other hand, Baculikova and Džurina [13] extended Equation (1) to include more models, as shown in the following equation…”