Periodic solutions for equation \(\dot x = A(t)x^m + B(t)x^n + C(t)x^l\) with \(A(t)\) and \(B(t)\) changing signs

DOI10.1016/j.jde.2012.03.021zbMath1277.34047OpenAlexW2314279115MaRDI QIDQ423593

Yulin Zhao, Jianfeng Huang

Publication date: 4 June 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2012.03.021

zbMATH Keywords

periodic solutionperiodic orbitAbel equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonautonomous smooth dynamical systems (37C60)

Related Items (13)

Uniqueness of limit cycles for quadratic vector fields ⋮ 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 ⋮ Existence of non-trivial limit cycles in Abel equations with symmetries ⋮ Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems ⋮ Limit cycles of Abel equations of the first kind ⋮ 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 ⋮ Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses ⋮ Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields ⋮ 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

Cites Work

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• Cubic systems and Abel equations
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• On a Class of Differential Equations of Riccati Type
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• The Bautin ideal of the Abel equation
• Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees
• Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
• The Number of Periodic Solutions of the Equation Ż=z ^N +p ₁ (t )z ^{N −1} +…+p _N (t )
• LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
• LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS

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