Rational solutions and limit cycles of polynomial and trigonometric Abel equations

The study the Abel differential equation x ′ = A ( t ) x 3 + B ( t ) x 2 + C ( t ) x . Specifically, we find bounds on the number of its rational solutions when A ( t ) , B ( t ) and C ( t ) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A ( t ) ,...

Full description

Saved in:
Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2025; no. 18; pp. 1 - 16
Main Author Calderón, Luis Ángel
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2025
Subjects
abel equation
invariant curve
limit cycle
Online AccessGet full text

Cover

More Information
Summary:The study the Abel differential equation x ′ = A ( t ) x 3 + B ( t ) x 2 + C ( t ) x . Specifically, we find bounds on the number of its rational solutions when A ( t ) , B ( t ) and C ( t ) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A ( t ) , B ( t ) and C ( t ) are trigonometric polynomials with real coefficients.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2025.1.18