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Further results on global stability of solutions of certain third-order nonlinear differential equations. (English) Zbl 1177.34072
The author considers the differential equation of the form \[ x''' + \psi (x,x',x'')x'' + f(x,x') = 0 \tag{1} \] or its equivalent system \[ x' = y, \quad y' = z, \quad z' = - \psi (x,y,z)z - f(x,y), \] in which \(\psi ,\psi _x ,\psi _y \in C(\mathbb R \times \mathbb R \times \mathbb R ,\mathbb R)\), \(f,f_x ,f_y \in C(\mathbb R \times \mathbb R ,\mathbb R)\) 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.

MSC:
34D23 Global stability of solutions to ordinary differential equations
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References:
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