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Qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method. (English) Zbl 1121.34039
The authors study systems of ordinary differential equations of the form
\[ \dot x = y,\quad \dot y = \sum_{k=0}^nf_k(x)y^k. \] They prove theorems that guarantee existence or non-existence of a limit cycle surrounding the origin via the comparison method.

MSC:
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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