Corpus ID: 237532415

Rational Solutions of Abel Differential Equations

  title={Rational Solutions of Abel Differential Equations},
  author={Jennifer Bravo and Lucas A. Calder{\'o}n and M. Fernandez and Ignacio Ojeda},
We study the rational solutions of the Abel equation x′ = A(t)x + B(t)x where A,B ∈ C[t]. We prove that if deg(A) is even or deg(B) > (deg(A) − 1)/2 then the equation has at most two rational solutions. For any other case, an upper bound on the number of rational solutions is obtained. Moreover, we prove that if there are more than (deg(A) + 1)/2 rational solutions then the equation admits a Darboux first integral. 


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