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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.

MSC:
34D20Stability of ODE
34C11Qualitative theory of solutions of ODE: growth, boundedness
34D05Asymptotic stability of ODE
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References:
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