Oscillation Criteria for Even-Order Nonlinear Dynamic Equations with Sublinear and Superlinear Neutral Terms on Time Scales

The symmetrical properties of dynamic and/or differential equations are kind of oscillation properties that allow us to conclude the character of solutions for dynamic equations. In this paper, we obtain some symmetrical properties of solutions to an even-order nonlinear dynamic equations with superlinear and sublinear neutral terms on time scales. Our approach is based on linearizing the considered equation in the sense that we would deduce the properties of the considered equation from that of the linear form and provide new oscillation results via comparing with first order as well as \(n\text {th}\) $n\text{th}$ order non-neutral delay dynamic inequalities. The new obtained results outfit a general podium that enables to analyse the oscillatory behaviour for many types of even-order nonlinear dynamic equations. An example is provided to demonstrate the validity of the theoretical outcomes.