×

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

MSC:

34D20 Stability of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[1] W. Magnus - S. WINKLER, Hill’s Equation , pp. 1 - 127 , Interscience , New York ( 1966 ). MR 197830 | Zbl 0158.09604 · Zbl 0158.09604
[2] G. Zampieri , Liapunov stability for some central forces , J. Differential Equations , 74 , n. 2, pp. 254-265 ( 1988 ). MR 952898 | Zbl 0668.34051 · Zbl 0668.34051
[3] G. Zampifri , Some problems in stability of the equilibrium related to coexistence of solutions to Hill’s equations, in the Proceedings of the Equadiff. 87 , Lecture Notes in Pure and Applied Mathematics , Dekker , Zbl 0685.34060 · Zbl 0685.34060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.