Lower bounds for the number of limit cycles of trigonometric Abel equations

DOI10.1016/j.jmaa.2007.12.016zbMath1362.34068OpenAlexW1984301218MaRDI QIDQ2481878

Armengol Gasull, Jiang Yu, Maria Jesus Alvarez

Publication date: 15 April 2008

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

Full work available at URL: http://ddd.uab.cat/record/44189

zbMATH Keywords

periodic orbitAbel equationMelnikov functions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23)

Related Items (13)

Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Rational Periodic Solutions on Some Generalized Abel Equations ⋮ LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ A new Chebyshev family with applications to Abel equations ⋮ Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses ⋮ Rational limit cycles of Abel equations ⋮ Some open problems in low dimensional dynamical systems ⋮ On the Number of Limit Cycles in Generalized Abel Equations ⋮ Periodic orbits from second order perturbation via rational trigonometric integrals ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations ⋮ On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones

Cites Work

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• Chebyshev property of complete elliptic integrals and its application to Abelian integrals.
• A new uniqueness criterion for the number of periodic orbits of Abel equations
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Limit Cycles for a Class of Abel Equations
• Mathematical problems
• Centennial History of Hilbert's 16th Problem
• Non-autonomous equations related to polynomial two-dimensional systems

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