Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument

Abstract

We present new oscillation criteria for the even order neutral delay differential equations with distributed deviating argument ${\left[r\left(t\right)\psi \left(x\left(t\right)\right)Z^{\left(n-1\right)}\left(t\right)\right]}^{\prime }+{\displaystyle {\int }_a^{b}p\left(t,\xi \right)}f\left[x\left(g\left(t,\xi \right)\right)\right]d\sigma \left(\xi \right)=0,t\ge t_0$, where $Z\left(t\right)=x\left(t\right)+q\left(t\right)x\left(t-\tau \right)$. Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those by Wang et al. (2005).