Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations

Abstract

New oscillation criteria are established for the second-order nonlinear neutralfunctional differential equations of the form ${(r(t){|z^{\prime }(t)|}^{\alpha -1}{z}^{\prime }(t))}^{’}+f(t,x[\sigma (t)])=0$, $t\ge t_0$, where $z(t)=x(t)+p(t)x(\tau (t))$, $p\in C^1([t_0,\infty ),[0,\mathrm{\infty }))$, and $\alpha \ge 1$. Our results improve andextend some known results in the literature. Some examples are also provided to show theimportance of these results.