Liouvillian first integrals for liénard polynomial differential systems

J. Llibre, C. Valls

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)


We characterize the Liouvillian first integrals for the Liénard polynomial differential systems of the form x′ = y, y′ = -cx - f(x)y, with c ∈ ℝ and f(x) is an arbitrary polynomial. For obtaining this result we need to find all the Darboux polynomials and the exponential factors of these systems. © 2010 American Mathematical Society.
Original languageEnglish
Pages (from-to)3229-3239
JournalProceedings of the American Mathematical Society
Issue number9
Publication statusPublished - 1 Sep 2010


  • Darboux polynomials
  • Exponential factors
  • Liénard polynomial differential systems
  • Liouvillian first integrals


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