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Zbl 1177.34072
Omeike, Mathew Omonigho
Further results on global stability of solutions of certain third-order nonlinear differential equations.
(English)
[J] Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 47, 121-127 (2008). ISSN 0231-9721

The author considers the differential equation of the form $$x''' + \psi (x,x',x'')x'' + f(x,x') = 0 \tag1$$ or its equivalent system $$x' = y, \quad y' = z, \quad z' = - \psi (x,y,z)z - f(x,y),$$ in which $\psi ,\psi _x ,\psi _y \in C(\Bbb R \times \Bbb R \times \Bbb R ,\Bbb R)$, $f,f_x ,f_y \in C(\Bbb R \times \Bbb R ,\Bbb R)$ and $f(0,0) = 0$. By defining an appropriate Lyapunov function, the author establishes some sufficient conditions which guarantee the globally asymptotically stability of the zero solution of (1). An example is also presented for illustration of the topic.
[Cemil Tunç (Van)]
MSC 2000:
*34D23 Global stability

Keywords: global stability; nonlinear differential equations; third order

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