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Zbl 1162.34043
Tunç, Cemil
On the stability and boundedness of solutions of nonlinear vector differential equations of third order. (English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 6, A, 2232-2236 (2009). ISSN 0362-546X

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 $p$.\par The proofs are based on the construction of suitable Lyapunov functions.
[Klaus R. Schneider (Berlin)]

MSC 2000:: *34D20 Lyapunov stability of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.
34D05 Asymptotic stability of ODE

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

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