Oscillation of second order neutral delay differential equations

J. Džurina; D. Hudáková

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 1, page 31-38
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Džurina, J., and Hudáková, D.. "Oscillation of second order neutral delay differential equations." Mathematica Bohemica 134.1 (2009): 31-38. <http://eudml.org/doc/38070>.

@article{Džurina2009,
abstract = {We establish some new oscillation criteria for the second order neutral delay differential equation \[ [r(t)|[x(t)+p(t)x[\tau (t)]]^\{\prime \}|^\{\alpha -1\} [x(t)+ p(t)x[\tau (t)]]^\{\prime \}]^\{\prime \} +\,q(t)f(x[\sigma (t)])=0. \] 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.},
author = {Džurina, J., Hudáková, D.},
journal = {Mathematica Bohemica},
keywords = {differential equation; oscillation; second order; delay; neutral type; integral averaging method; neutral type; integral averaging method},
language = {eng},
number = {1},
pages = {31-38},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of second order neutral delay differential equations},
url = {http://eudml.org/doc/38070},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Džurina, J.
AU - Hudáková, D.
TI - Oscillation of second order neutral delay differential equations
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 1
SP - 31
EP - 38
AB - We establish some new oscillation criteria for the second order neutral delay differential equation \[ [r(t)|[x(t)+p(t)x[\tau (t)]]^{\prime }|^{\alpha -1} [x(t)+ p(t)x[\tau (t)]]^{\prime }]^{\prime } +\,q(t)f(x[\sigma (t)])=0. \] 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.
LA - eng
KW - differential equation; oscillation; second order; delay; neutral type; integral averaging method; neutral type; integral averaging method
UR - http://eudml.org/doc/38070
ER -

References

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