Oscillation theory of third-order nonlinear functional differential equations

Abstract

In this paper, we are concerned with oscillation of solutions of a certain class of third-order nonlinear delay differential equations of the form $% x^{^{\prime \prime \prime }}(t)+p(t)x^{^{\prime}}(t)+q(t)f(x(\tau (t)))=0$. We establish some new oscillation results that extend and improve some results in the literature in the sense that our results do not require that $% \tau ^{^{\prime }}(t)\geq 0$. Some examples are considered to illustrate the main results and some conjectures and open problems are presented.