Limit cycles of Abel equations of the first kind

DOI10.1016/j.jmaa.2014.10.019zbMath1326.34027OpenAlexW1992538858MaRDI QIDQ465441

J. Herrera, D. Rodríguez-Gómez

Publication date: 31 October 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.10.019

zbMATH Keywords

periodic solutionslimit cyclesAbel equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34)

Related Items (15)

Kink solitary solutions to generalized Riccati equations with polynomial coefficients ⋮ Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities ⋮ Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities ⋮ Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves ⋮ Periodic solutions of Abel equations with jumps ⋮ Upper bounds of limit cycles in Abel differential equations with invariant curves ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Anti-periodic solutions of Abel differential equations with state dependent discontinuities ⋮ Rational limit cycles of Abel equations ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions ⋮ On the Number of Limit Cycles in Generalized Abel Equations ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations

Uses Software

• Mathematica

Cites Work

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