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

Blanka Baculíková; Jozef Džurina

Open Mathematics (2010)

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

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topBlanka 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 -

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