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Further results on global stability of third-order nonlinear differential equations. (English) Zbl 1129.34323
Consider the differential equation \[ x'''+\psi(x,x')x''+f(x,x')=0\tag{*} \] with \(f(0,0)=0\) and where \(\psi,f,f_x,\psi_x\) are continuous. The author derives conditions for the global asymptotical stability of the trivial solution of (*) improving known results.

MSC:
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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