On the asymptotic behavior of a class of third order nonlinear neutral differential equations

Blanka Baculíková; Jozef Džurina

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In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation $L_{n} u (t) + p (t) f (u [g (t)]) = 0$ are compared with those of the functional differential equation $α_{n} u (t) + q (t) h (u [w (t)]) = 0$ .

Oscillation of second order neutral delay differential equations

J. Džurina, D. Hudáková (2009)

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We establish some new oscillation criteria for the second order neutral delay differential equation ${[r (t) | [x (t) + p (t) x [τ (t)]]}^{'} {|^{α - 1} {[x (t) + p (t) x [τ (t)]]}^{'}]}^{'} + q (t) f (x [σ (t)]) = 0 .$ The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.