On the oscillation of third-order quasi-linear neutral functional differential equations

Ethiraju Thandapani; Tongxing Li

Archivum Mathematicum (2011)

  • Volume: 047, Issue: 3, page 181-199
  • ISSN: 0044-8753

Abstract

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The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation [ a ( t ) ( [ x ( t ) + p ( t ) x ( δ ( t ) ) ] ' ' ) α ] ' + q ( t ) x α ( τ ( t ) ) = 0 , E where α > 0 , 0 ≤ p ( t ) ≤ p 0 < ∞ and δ ( t ) ≤ t . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.

How to cite

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Thandapani, Ethiraju, and Li, Tongxing. "On the oscillation of third-order quasi-linear neutral functional differential equations." Archivum Mathematicum 047.3 (2011): 181-199. <http://eudml.org/doc/246122>.

@article{Thandapani2011,
abstract = {The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation \begin\{equation*\} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^\{\prime \prime \}\big )^\alpha \big ]^\{\prime \}+q(t)x^\alpha (\tau (t))=0\,, E \end\{equation*\} where $\alpha >0$, $0\le p(t)\le p_0<\infty $ and $\delta (t)\le t$. By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.},
author = {Thandapani, Ethiraju, Li, Tongxing},
journal = {Archivum Mathematicum},
keywords = {third-order; neutral functional differential equations; oscillation and asymptotic behavior; third-order neutral functional differential equation; oscillation; asymptotic behavior},
language = {eng},
number = {3},
pages = {181-199},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the oscillation of third-order quasi-linear neutral functional differential equations},
url = {http://eudml.org/doc/246122},
volume = {047},
year = {2011},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Li, Tongxing
TI - On the oscillation of third-order quasi-linear neutral functional differential equations
JO - Archivum Mathematicum
PY - 2011
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 047
IS - 3
SP - 181
EP - 199
AB - The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation \begin{equation*} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^{\prime \prime }\big )^\alpha \big ]^{\prime }+q(t)x^\alpha (\tau (t))=0\,, E \end{equation*} where $\alpha >0$, $0\le p(t)\le p_0<\infty $ and $\delta (t)\le t$. By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.
LA - eng
KW - third-order; neutral functional differential equations; oscillation and asymptotic behavior; third-order neutral functional differential equation; oscillation; asymptotic behavior
UR - http://eudml.org/doc/246122
ER -

References

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  12. Saker, S. H., Džurina, J., On the oscillation of certain class of third-order nonlinear delay differential equations, Math. Bohem. 135 (2010), 225–237. (2010) Zbl1224.34217MR2683636
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