An Upper Bound for the Number of Rational Solutions of Generalized Abel Equations

• Hui Zeng ^[1] ; Yulin Zhao ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 3, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper is concerned with the non-trivial rational solutions for the generalized Abel equation x = A(t)xn + B(t)xm + C(t)x, where m, n ∈ N, n > m > 1 and A(t), B(t),C(t) ∈ R[t]. A solution is called a non-trivial rational solution if it takes the form x = q(t)/p(t), where p, q are polynomials in t and gcd(p, q) = 1 with deg(p) ≥ 1. In this work, we provide an upper bound on the number of the real and complex non-trivial rational solutions for the mentioned generalized Abel equation.

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