Displaying similar documents to “Oscillation of second order neutral delay differential equations”

On unstable neutral differential equations of the second order

Jozef Džurina (2002)

Czechoslovak Mathematical Journal

Similarity:

The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation ( x ( t ) - p x ( t - τ ) ) ' ' - q ( t ) x ( σ ( t ) ) = 0 to be oscillatory and to improve some existing results. The main results are based on the comparison principles.

Oscillation theorems for certain even order neutral differential equations

Qi Gui Yang, Sui-Sun Cheng (2007)

Archivum Mathematicum

Similarity:

This paper is concerned with a class of even order nonlinear differential equations of the form d d t | x ( t ) + p ( t ) x ( τ ( t ) ) ( n - 1 ) | α - 1 ( x ( t ) + p ( t ) x ( τ ( t ) ) ) ( n - 1 ) + F ( t , x ( g ( t ) ) ) = 0 , where n is even and t ≥ t 0 . By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.

Oscillation of the third order Euler differential equation with delay

Blanka Baculíková, Jozef Džurina (2014)

Mathematica Bohemica

Similarity:

In the paper we offer criteria for oscillation of the third order Euler differential equation with delay y ' ' ' ( t ) + k 2 t 3 y ( c t ) = 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.