# Unbounded solutions of third order delayed differential equations with damping term

Miroslav Bartušek; Mariella Cecchi; Zuzana Došlá; Mauro Marini

Open Mathematics (2011)

- Volume: 9, Issue: 1, page 184-195
- ISSN: 2391-5455

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topMiroslav Bartušek, et al. "Unbounded solutions of third order delayed differential equations with damping term." Open Mathematics 9.1 (2011): 184-195. <http://eudml.org/doc/269643>.

@article{MiroslavBartušek2011,

abstract = {Globally positive solutions for the third order differential equation with the damping term and delay, \[ x^\{\prime \prime \prime \} + q(t)x^\{\prime \}(t) - r(t)f(x(\phi (t))) = 0, \]
are studied in the case where the corresponding second order differential equation \[ y^\{\prime \prime \} + q(t)y = 0 \]
is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those in the case when (**) is nonoscillatory is given, as well.},

author = {Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini},

journal = {Open Mathematics},

keywords = {Third order differential equation; Delay; Damping term; Globally positive solution; Unbounded solutions; Oscillation; third order differential equation; delay; damping term; globally positive solution; unbounded solutions; oscillation},

language = {eng},

number = {1},

pages = {184-195},

title = {Unbounded solutions of third order delayed differential equations with damping term},

url = {http://eudml.org/doc/269643},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Miroslav Bartušek

AU - Mariella Cecchi

AU - Zuzana Došlá

AU - Mauro Marini

TI - Unbounded solutions of third order delayed differential equations with damping term

JO - Open Mathematics

PY - 2011

VL - 9

IS - 1

SP - 184

EP - 195

AB - Globally positive solutions for the third order differential equation with the damping term and delay, \[ x^{\prime \prime \prime } + q(t)x^{\prime }(t) - r(t)f(x(\phi (t))) = 0, \]
are studied in the case where the corresponding second order differential equation \[ y^{\prime \prime } + q(t)y = 0 \]
is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those in the case when (**) is nonoscillatory is given, as well.

LA - eng

KW - Third order differential equation; Delay; Damping term; Globally positive solution; Unbounded solutions; Oscillation; third order differential equation; delay; damping term; globally positive solution; unbounded solutions; oscillation

UR - http://eudml.org/doc/269643

ER -

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