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Zbl 1132.34328
Tunç, Cemil; Ateş, Muzaffer
Stability and boundedness results for solutions of certain third order nonlinear vector differential equations.
(English)
[J] Nonlinear Dyn. 45, No. 3-4, 273-281 (2006). ISSN 0924-090X; ISSN 1573-269X/e

Consider the nonlinear vector differential equation $$\dddot x+F(x, \dot x,\ddot x)\ddot x+B(t)\dot x+h(\dot x)=p(t,x,\dot x,\ddot x), \quad t\ge 0, \tag*$$ where $F$ and $B$ are symmetric $n\times n$-matrices depending continuously on their arguments, the functions $h$ and $p$ mapping into $\bbfR^n$ 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.
[Klaus R. Schneider (Berlin)]
MSC 2000:
*34D20 Lyapunov stability of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.

Keywords: boundedness; differential equation of third order; Lyapunov function; stability

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