Oscillation criteria for even order nonlinear neutral differential equations

Abstract

In this paper, we consider the oscillation criteria for even order nonlinear neutral differential equations of the form $$ \left(r(t)z^{(n-1)}(t)\right)'+q(t)f(x(\sigma(t)))=0, $$ where $z(t)=x(t)+p(t)x(\tau(t)),$ $n\geq2$ is a even integer. The results are obtained both for the case $\int^\infty r^{-1}(t){\rm d}t=\infty,$ and in case $\int^\infty r^{-1}(t){\rm d}t<\infty.$ These criteria here derived extend and improve some known results in literatures. Some examples are given to illustrate our main results.