Periodic Solutions of Abel Differential Equations

Details Periodic Solutions of Abel Differential Equations Periodic Solutions of Abel Differential Equations

2006-05-05

arxiv.org/abs/math/0605153v2

Mathematics

Classical Analysis and ODEs

Scientific paper

For a class of polynomial non-autonomous differential equations of degree n,
we use phase plane analysis to show that each equation in this class has n
periodic solutions. The result implies that certain rigid two-dimensional
systems have at most one limit cycle which appears through multiple Hopf
bifurcation.

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