Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform

In this paper, we obtain sufficient conditions for the third-order nonlinear advanced differential equation (a₂(t)(a₁(t)y′(t))′)^{′α}(σ(t)) with ∫_{t₀}^{∞}(1/(a₂(t)))dtwith $$\int_{t_0}^{\infty}\frac{1}{a_2(t)}dt<\infty\;\text{and}\;\int_{t_0}^{\infty}\frac{1}{a_1(t)}dt<\infty,$$ to have property B or to be oscillatory. This is achieved by transforming the studied equation into canonical type and then using integral averaging method. Examples are provided to illustrate the main results.