Oscillation of third order differential equation with damping term

Miroslav Bartušek; Zuzana Došlá

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 301-316
  • ISSN: 0011-4642

Abstract

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We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term x ' ' ' ( t ) + q ( t ) x ' ( t ) + r ( t ) | x | λ ( t ) sgn x ( t ) = 0 , t ≥ 0 . We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case λ ≤ 1 and if the corresponding second order differential equation h ' ' + q ( t ) h = 0 is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.

How to cite

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Bartušek, Miroslav, and Došlá, Zuzana. "Oscillation of third order differential equation with damping term." Czechoslovak Mathematical Journal 65.2 (2015): 301-316. <http://eudml.org/doc/270123>.

@article{Bartušek2015,
abstract = {We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term \[ x^\{\prime \prime \prime \}(t)+q(t)x^\{\prime \}(t)+r(t)|x|^\{\lambda \}(t)\mathop \{\rm sgn\} x(t)=0 ,\quad t\ge 0. \] We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $\lambda \le 1$ and if the corresponding second order differential equation $h^\{\prime \prime \}+q(t)h=0$ is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.},
author = {Bartušek, Miroslav, Došlá, Zuzana},
journal = {Czechoslovak Mathematical Journal},
keywords = {third order nonlinear differential equation; vanishing at infinity solution; Kneser solution; oscillatory solution},
language = {eng},
number = {2},
pages = {301-316},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of third order differential equation with damping term},
url = {http://eudml.org/doc/270123},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Bartušek, Miroslav
AU - Došlá, Zuzana
TI - Oscillation of third order differential equation with damping term
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 301
EP - 316
AB - We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term \[ x^{\prime \prime \prime }(t)+q(t)x^{\prime }(t)+r(t)|x|^{\lambda }(t)\mathop {\rm sgn} x(t)=0 ,\quad t\ge 0. \] We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $\lambda \le 1$ and if the corresponding second order differential equation $h^{\prime \prime }+q(t)h=0$ is oscillatory, we also study Kneser solutions vanishing at infinity and the existence of oscillatory solutions.
LA - eng
KW - third order nonlinear differential equation; vanishing at infinity solution; Kneser solution; oscillatory solution
UR - http://eudml.org/doc/270123
ER -

References

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