In this paper we study asymptotic properties of the third order trinomial delay differential equation $$ y'''(t)-p(t)y'(t)+g(t)y(\tau (t))= 0 $$ by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.
In the paper we offer criteria for oscillation of the third order Euler differential equation with delay y ′′′(t) + k 2 ⁄ t 3 y(ct) = 0. We provide detail analysis of the properties of this equation, we fill the gap in the oscillation theory and provide necessary and sufficient conditions for oscillation of equation considered.
The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument (x(t) − px(t − τ ))'' − q(t)x(σ(t)) = 0. The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered.
In this paper we present some new oscillatory criteria for the $n$-th order neutral differential equations of the form \[ (x(t)\pm p(t)x[\tau (t)])^{(n)} +q(t)x[\sigma (t)] =0. \] The results obtained extend and improve a number of existing criteria.