Oscillation of third order differential equation with damping term

• Published in: Czechoslovak mathematical journal Vol. 65; no. 2; pp. 301 - 316
• Main Authors: Bartušek, Miroslav, Došlá, Zuzana
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2015
• Subjects: Analysis; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; 34C15; Kneser solution; 34C10; vanishing at infinity solution; third order nonlinear differential equation; oscillatory solution
• ISSN: 0011-4642; 1572-9141
• DOI: 10.1007/s10587-015-0176-3

We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term
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.