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Tunç, Cemil; Ateş, Muzaffer

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

Nonlinear Dyn. 45, No. 3-4, 273-281 (2006).
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.
Reviewer: Klaus R. Schneider (Berlin)

Cited in 1 Review
Cited in 16 Documents

MSC:

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

Keywords:

boundedness; differential equation of third order; Lyapunov function; stability
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\textit{C. Tunç} and \textit{M. Ateş}, Nonlinear Dyn. 45, No. 3--4, 273--281 (2006; Zbl 1132.34328)
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References:

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