Geodesic
Instability of solutions of certain nonlinear vector differential equations of third order
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 34D20, 34C25, 34A34
Keywords: nonlinear differential equations of third order, instability, periodic solution, Lyapunov's method 
@article{EJDE_2005__2005__a92,
     author = {Tun\c{c},  Ercan},
     title = {Instability of solutions of certain nonlinear vector differential equations of third order},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a92/}
}
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JO  - Electronic journal of differential equations
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VL  - 2005
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%T Instability of solutions of certain nonlinear vector differential equations of third order
%J Electronic journal of differential equations
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%F EJDE_2005__2005__a92
Tunç,  Ercan. Instability of solutions of certain nonlinear vector differential equations of third order. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a92/