Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 51, pp. 1-6.

Title: Instability of solutions of certain nonlinear 
       vector differential equations of third order 
       
Author: Ercan Tunc (Gaziosmanpasa Univ., Turkey)

Abstract: 
 In this paper, study the system of differential equations
 $$
 \dddot{X}+F(\dot{X})\ddot{X}+G(X)\dot{X} +H(X,\dot{X},\ddot{X})=0\,.
 $$
 We find sufficient conditions for  the zero solution to be unstable,
 and to be the only periodic solution.
 
Submitted March 14, 2005. Published May 11, 2005.
Math Subject Classifications: 34D20, 34C25, 34A34.
Key Words: Nonlinear differential equations of third order;  
           instability; periodic solution; Lyapunov's method.