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

Abstract

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Globally positive solutions for the third order differential equation with the damping term and delay, x ' ' ' + q ( t ) x ' ( t ) - r ( t ) f ( x ( φ ( t ) ) ) = 0 , are studied in the case where the corresponding second order differential equation y ' ' + 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.

How to cite

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Miroslav 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 -

References

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