Solving a collection of free coexistence-like problems in stability. (English) Zbl 0683.34033

The aim of the paper is to find all the \(C^ 1\) real maps f, defined in a neighbourhood of \(0\in {\mathbb{R}}\), such that the origin is Lyapunov stable for the system \[ \frac{d^ 2}{dt^ 2}x=g(x),\quad \frac{d^ 2}{dt^ 2}y=y(g'(x)+\frac{3\alpha g(x)}{1+\alpha x}),\quad x,y\in {\mathbb{R}}, \] where \(g(x)=-xf(x)\) and \(\alpha\in {\mathbb{R}}\).
Reviewer: G.Zampieri


34D20 Stability of solutions to ordinary differential equations
Full Text: Numdam EuDML


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