## Stability and boundedness results for solutions of certain third order nonlinear vector differential equations.(English)Zbl 1132.34328

Consider the nonlinear vector differential equation
$\dddot x+F(x, \dot x,\ddot x)\ddot x+B(t)\dot x+h(\dot x)=p(t,x,\dot x,\ddot x), \quad t\geq 0, \tag{*}$ where $$F$$ and $$B$$ are symmetric $$n\times n$$-matrices depending continuously on their arguments, the functions $$h$$ and $$p$$ mapping into $$\mathbb{R}^n$$ are also continuous functions. Using Lyapunov’s direct method, the authors present conditions guaranteeing the asymptotic stability of the zero solution of (*) and the boundedness of all solutions.

### MSC:

 34D20 Stability of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
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### References:

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