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arxiv: math/0411042 · v1 · submitted 2004-11-02 · 🧮 math.CA · math.DS

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

classification 🧮 math.CA math.DS
keywords phase--portraituniquenessanalysisclassclassicalcomparisonconcerningcycles
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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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