Oscillation Results for Third-Order Semi-Canonical Quasi-Linear Delay Differential Equations

The main purpose of this paper is to study the oscillatory properties of solutions of the third-order quasi-linear delay differential equation ℒy(t)+f(t)yβ(σ(t))=0{\cal L}y(t) + f(t){y^\beta }(\sigma (t)) = 0 where ℒy(t) = (b(t)(a(t)(y0(t)) )0)0 is a semi-canonical differential operator. The main idea is to transform the semi-canonical operator into canonical form and then obtain new oscillation results for the studied equation. Examples are provided to illustrate the importance of the main results.