Geodesic
Oscillation of third order differential equation with damping term
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 301-316

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We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $$ x'''(t)+q(t)x'(t)+r(t)|x|^{\lambda }(t)\mathop {\rm sgn} x(t)=0 ,\quad t\geq 0. $$ 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.
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.
DOI : 10.1007/s10587-015-0176-3
Classification : 34C10, 34C15
Keywords: third order nonlinear differential equation; vanishing at infinity solution; Kneser solution; oscillatory solution 
Bartušek, Miroslav; Došlá, Zuzana. Oscillation of third order differential equation with damping term. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 301-316. doi: 10.1007/s10587-015-0176-3
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     pages = {301--316},
     year = {2015},
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     language = {en},
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