Browsing Articles publicats (Matemàtica) by Subject "Rational first integral"

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Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential systems

Giné, Jaume; Grau Montaña, Maite; Llibre, Jaume (American Institute of Mathematical Sciences, 2013-10)

In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous ...
The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations

Giné, Jaume; Llibre, Jaume (Elsevier, 2023)

In this work we classify the polynomial Liénard differential equations ̈𝑥 + 𝑓(𝑥) ̇𝑥 + 𝑥 = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential ...