The generalized Liénard polynomial differential systems \(x^\prime = y\), \(y^\prime = - g(x) - f(x) y\) with \(\deg g = \deg f + 1\) are not Liouvillian integrable

DOI10.1016/j.bulsci.2014.08.010zbMath1406.34045OpenAlexW2010832332MaRDI QIDQ1756316

Jaume Llibre, Claudia Valls

Publication date: 14 January 2019

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2014.08.010

zbMATH Keywords

Darboux polynomialsexponential factorsLiouvillian first integralsLiénard polynomial differential systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Invariant manifolds for ordinary differential equations (34C45)

Related Items (4)

Liouvillian integrability versus Darboux polynomials ⋮ A note on: ``The generalized Liénard polynomial differential systems \(x' = y\), \(y' =-g(x) - f(x)y\), with \(\deg g =\deg f + 1\), are not Liouvillian integrable ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

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• Liouvillian First Integrals of Differential Equations
• On the polynomial first integrals of the (a,b,c) Lotka–Volterra system
• Liouvillian first integrals for Liénard polynomial differential systems

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