Oscillation of third order differential equation with damping term

Title:

Oscillation of third order differential equation with damping term

Creator:

Bartušek, Miroslav and Došlá, Zuzana

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e4b6132b-3b79-4ac8-9c12-c9a84cf14f87
uuid:e4b6132b-3b79-4ac8-9c12-c9a84cf14f87

Subject:

third order nonlinear differential equation, vanishing at infinity solution, Kneser solution;, and oscillatory soluton

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $$ x'''(t)+q(t)x'(t)+r(t)|x|^{\lambda }(t)\mathop {\rm sgn} x(t)=0 ,\quad t\geq 0. $$ We give conditions under which every solution of the equation above is either oscillatory or tends to zero. In case $\lambda \leq 1$ 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

301-316

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:2

Harvested from:

CDK

Metadata only:

false