New oscillation criteria for second order delay differential equations with non-positive neutral term

Abstract

In this paper we obtain some new oscillation criteria for the neutral differential equation of the form
$$\left(r(t)(x(t)-p(t)x(\tau(t)))' \right)'+q(t)f(x(\sigma(t)))=0,~~t\geq t_0>0$$
where $0\leq p(t)\leq p_0<1$ and $q(t)>0$ for all $t\geq t_0$. The results presented in this paper extend and complement to some of the existing results. Examples are provided to illustrate the main results.