Some new results on Abel equations

DOI10.1006/jmaa.2001.7478zbMath0995.34031OpenAlexW2090189057MaRDI QIDQ5946933

Yun Tang, Li-Jun Yang

Publication date: 15 October 2002

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

Full work available at URL: https://doi.org/10.1006/jmaa.2001.7478

zbMATH Keywords

Bautin idealAbel differential equationcenter problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Periodic solutions of integral equations (45M15) Periodic orbits of vector fields and flows (37C27) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (10)

An explicit bound of the number of vanishing double moments forcing composition ⋮ On the center problem for generalized Abel equations ⋮ Conditions to the existence of center for Abel equations ⋮ Research on the properties of some planar polynomial differential equations ⋮ A partial positive answer to a Lijun-Yun conjecture ⋮ Cauchy-type integrals of algebraic functions ⋮ Center conditions at infinity for Abel differential equations ⋮ On the equivalence of differential equations in the sense of coincidence reflecting functions ⋮ On the center-focus problem for a family of high-order polynomial differential systems ⋮ On the uniqueness and expression of limit cycles in planar polynomial differential system via monotone iterative technique

Cites Work

• Unnamed Item
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Cubic systems and Abel equations
• Center conditions. III: Parametric and model center problems
• A class of recursive formulas on the calculation of focus values
• Word problems related to periodic solutions of a non-autonomous system
• Limit Cycles for a Class of Abel Equations
• Center conditions, compositions of polynomials and moments on algebraic curves
• The Bautin ideal of the Abel equation
• Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees
• Non-autonomous equations related to polynomial two-dimensional systems
• On a condition for a centre of cubic non-autonomous equations

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