1. Oscillation of third order differential equation with damping term
- Creator:
- Bartušek, Miroslav and Došlá, Zuzana
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- third order nonlinear differential equation, vanishing at infinity solution, Kneser solution;, and oscillatory soluton
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public