Oscillation of Third-Order Differential Equations with Mixed Arguments

Abstract

In this paper we establish new comparison theorems for deducing property (A) and the oscillation of the third-order nonlinear functional differential equation with mixed arguments

$$\displaystyle{ \left [a(t){\left [x^{\prime}(t)\right ]}^{\gamma }\right ]^{\prime\prime} + q(t)f(x\left [\tau (t)\right ]) + p(t)h(x\left [\sigma (t)\right ]) = 0 }$$

from the oscillation of a set of suitable first-order delay/advanced equations under condition ${\int }^{\infty }{a}^{-1/\gamma }(s)\,\mathrm{d}s = \infty$.