Property $ \bar{A} $ of third-order noncanonical functional differential equations with positive and negative terms

Abstract

In this article, we have derived a new method to study the oscillatory and asymptotic properties for third-order noncanonical functional differential equations with both positive and negative terms of the form $ \begin{equation*} (p_2 (t)(p_1 (t) x'(t) )')'+a(t)g(x(\tau(t)))-b(t)h(x(\sigma(t)) = 0 \end{equation*} $ Firstly, we have converted the above equation of noncanonical type into the canonical type using the strongly noncanonical operator and obtained some new conditions for Property $ \bar{A} $. We furnished illustrative examples to validate our main result.

Keywords

• property $ \bar{a} $
• third-order
• noncanonical
• delay argument