Qualitative analysis of phase--portrait for a class of planar vector fields via the comparison method

Details Qualitative analysis of phase--portrait for a class of planar vector fields via the comparison method Qualitative analysis of phase--portrait for a class of planar vector fields via the comparison method

2004-11-02

arxiv.org/abs/math/0411042v1

Mathematics

Classical Analysis and ODEs

5 figures

Scientific paper

The phase--portrait of the second order differential equation: $$\ddot
x+\sum_{l=0}^nf_l(x) \dot x^l=0 ,$$ is studied. Some results concerning
existence, non--existence and uniqueness of limit cycles are presented. Among
these, a generalization of the classical Massera uniqueness result is proved.

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