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

Open Mathematics (2010)

• Volume: 8, Issue: 6, page 1091-1103
• ISSN: 2391-5455

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## Abstract

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The objective of this paper is to study asymptotic properties of the third-order neutral differential equation ${\left[a\left(t\right){\left({\left[x\left(t\right)+p\left(t\right)x\left(\sigma \left(t\right)\right)\right]}^{\text{'}\text{'}}\right)}^{\gamma }\right]}^{\text{'}}+q\left(t\right)f\left(x\left[\tau \left(t\right)\right]\right)=0,t⩾{t}_{0}.\left(E\right)$ . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.

## How to cite

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Blanka Baculíková, and Jozef Džurina. "On the asymptotic behavior of a class of third order nonlinear neutral differential equations." Open Mathematics 8.6 (2010): 1091-1103. <http://eudml.org/doc/269611>.

@article{BlankaBaculíková2010,
abstract = {The objective of this paper is to study asymptotic properties of the third-order neutral differential equation $\left[ \{a\left( t \right)\left( \{\left[ \{x\left( t \right) + p\left( t \right)x\left( \{\sigma \left( t \right)\} \right)\} \right]^\{\prime \prime \} \} \right)^\gamma \} \right]^\prime + q\left( t \right)f\left( \{x\left[ \{\tau \left( t \right)\} \right]\} \right) = 0, t \geqslant t\_0 . \left( E \right)$ . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.},
author = {Blanka Baculíková, Jozef Džurina},
journal = {Open Mathematics},
keywords = {Third-order neutral differential equations; Oscillation; Nonoscillation; Comparison theorem; third-order neutral differential equations; oscillation; nonoscillation; comparison theorem},
language = {eng},
number = {6},
pages = {1091-1103},
title = {On the asymptotic behavior of a class of third order nonlinear neutral differential equations},
url = {http://eudml.org/doc/269611},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Blanka Baculíková
AU - Jozef Džurina
TI - On the asymptotic behavior of a class of third order nonlinear neutral differential equations
JO - Open Mathematics
PY - 2010
VL - 8
IS - 6
SP - 1091
EP - 1103
AB - The objective of this paper is to study asymptotic properties of the third-order neutral differential equation $\left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right)$ . We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.
LA - eng
KW - Third-order neutral differential equations; Oscillation; Nonoscillation; Comparison theorem; third-order neutral differential equations; oscillation; nonoscillation; comparison theorem
UR - http://eudml.org/doc/269611
ER -

## References

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