Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients

Julio G. Dix; Dillip Kumar Ghose; Radhanath Rath

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 4, page 411-425
  • ISSN: 0862-7959

Abstract

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We obtain sufficient conditions for every solution of the differential equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + v ( t ) G ( y ( g ( t ) ) ) - u ( t ) H ( y ( h ( t ) ) ) = f ( t ) to oscillate or to tend to zero as t approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when G has sub-linear growth at infinity. Our results also apply to the neutral equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + q ( t ) G ( y ( g ( t ) ) ) = f ( t ) when q ( t ) has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.

How to cite

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Dix, Julio G., Ghose, Dillip Kumar, and Rath, Radhanath. "Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients." Mathematica Bohemica 134.4 (2009): 411-425. <http://eudml.org/doc/38103>.

@article{Dix2009,
abstract = {We obtain sufficient conditions for every solution of the differential equation \[ [y(t)-p(t)y(r(t))]^\{(n)\}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t) \] to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation \[ [y(t)-p(t)y(r(t))]^\{(n)\}+q(t)G(y(g(t)))=f(t) \] when $q(t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.},
author = {Dix, Julio G., Ghose, Dillip Kumar, Rath, Radhanath},
journal = {Mathematica Bohemica},
keywords = {oscillatory solution; neutral differential equation; asymptotic behaviour; oscillatory solution; neutral differential equation; asymptotic behaviour},
language = {eng},
number = {4},
pages = {411-425},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients},
url = {http://eudml.org/doc/38103},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Dix, Julio G.
AU - Ghose, Dillip Kumar
AU - Rath, Radhanath
TI - Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 4
SP - 411
EP - 425
AB - We obtain sufficient conditions for every solution of the differential equation \[ [y(t)-p(t)y(r(t))]^{(n)}+v(t)G(y(g(t)))-u(t)H(y(h(t)))=f(t) \] to oscillate or to tend to zero as $t$ approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when $G$ has sub-linear growth at infinity. Our results also apply to the neutral equation \[ [y(t)-p(t)y(r(t))]^{(n)}+q(t)G(y(g(t)))=f(t) \] when $q(t)$ has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.
LA - eng
KW - oscillatory solution; neutral differential equation; asymptotic behaviour; oscillatory solution; neutral differential equation; asymptotic behaviour
UR - http://eudml.org/doc/38103
ER -

References

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