Neutral Differential Equations of Second-Order: Iterative Monotonic Properties

In this work, we investigate the oscillatory properties of the neutral differential equation (r(l)[(s(l)+p(l)s(g(l)))′]v)′+∑i=1nqi(l)sv(hi(l))=0, where s≥s0. We first present new monotonic properties for the solutions of this equation, and these properties are characterized by an iterative nature. Using these new properties, we obtain new oscillation conditions that guarantee that all solutions are oscillate. Our results are a complement and extension to the relevant results in the literature. We test the significance of the results by applying them to special cases of the studied equation.