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**On the stability and boundedness of solutions of nonlinear vector differential equations of third order.**
*(English)*
Zbl 1162.34043

Consider the vector differential equation
\[
{d^3 x\over dt^3}+ \Psi\Biggl({dx\over dt}\Biggr) {d^2 x\over dt^2}+ B{dx\over dt}+ cx= p(t),\tag{\(*\)}
\]
where \(B\) is a constant symmetric \(n\times n\)-matrix, \(c\) is a positive constant, \(\Psi\) is a continuous symmetric \(n\times n\)-matrix function. In case \(p\equiv 0\), the author proves a theorem on global asymptotic stability of the equilibrium \(x= 0\). His second theorem is concerned with boundedness of all solutions of \((*)\) under certain assumptions on \(p\).

The proofs are based on the construction of suitable Lyapunov functions.

The proofs are based on the construction of suitable Lyapunov functions.

Reviewer: Klaus R. Schneider (Berlin)

### MSC:

34D20 | Stability of solutions to ordinary differential equations |

34C11 | Growth and boundedness of solutions to ordinary differential equations |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

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\textit{C. Tunç}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 6, 2232--2236 (2009; Zbl 1162.34043)

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### References:

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