Second‐order oscillation of non‐canonical functional dynamical equations on time scales.

The goal of this paper is to study the oscillation of the following second‐order nonlinear functional dynamic equation [r(t)(yΔ(t))α]Δ+Υ(t)yβ(δ(t))=0,t∈𝕋0=[t0,∞)∩𝕋.The main aim is to establish the necessary and sufficient conditions for the oscillation of the equation. The results are obtained when α > β and α < β. At the end, examples are provided to illustrate the analytical findings. We point out that the results are new even for the case 𝕋=ℝ and 𝕋=ℤ. [ABSTRACT FROM AUTHOR]