Existence of non-trivial limit cycles in Abel equations with symmetries

DOI10.1016/j.na.2013.02.001zbMath1312.34079OpenAlexW1989482876MaRDI QIDQ388466

Mohammad Hasan, H. S. Yoon

Publication date: 19 December 2013

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150619

zbMATH Keywords

periodic solutionslimit cyclesAbel equationAbelian integrals

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27)

Related Items (14)

Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Centers and limit cycles for a family of 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 ⋮ 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 study and application of limit cycles of a kind of piecewise smooth equation ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations

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