Cemil Tunç and Hamdullah Şevli

On the Instability of Solutions of Certain Fifth Order Nonlinear Differential Equations

abstract:
The main purpose of this paper is to give sufficient conditions which guarantee the instability of the trivial solution of a nonlinear vector differential equation as follows:
\begin{equation*}
X^{(5)} + \Psi (\dot {X},\ddot {X})\dddot{X}+ \Phi (X,\dot
{X},\ddot {X}) + \Theta (\dot {X}) + F(X) = 0.
\end{equation*}

Mathematics Subject Classification: 34D05, 34D20

Key words and phrases: Nonlinear differential equations of fifth order, instability, Lyapunov's method