Weierstrass integrability in Liénard differential systems

DOI10.1016/j.jmaa.2010.11.005zbMath1229.34015OpenAlexW2053659998MaRDI QIDQ626181

Jaume Giné, Jaume Llibre

Publication date: 22 February 2011

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

Full work available at URL: http://ddd.uab.cat/record/150438

zbMATH Keywords

Weierstrass inverse integrating factorLiénard differential systemWeierstrass first integral

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (19)

Invariant algebraic curves for Liénard dynamical systems revisited ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ Generalized Weierstrass integrability of the Abel differential equations ⋮ Hopf bifurcation of limit cycles in discontinuous Liénard systems ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Formal Weierstrass Nonintegrability Criterion for Some Classes of Polynomial Differential Systems in ℂ2 ⋮ Liénard Equation and Its Generalizations ⋮ Linearizabiliy and Lax representations for cubic autonomous and non-autonomous nonlinear oscillators ⋮ The application of Liénard transformations to predator-prey systems ⋮ On the geometric and analytical properties of the anharmonic oscillator ⋮ Invariant algebraic curves for certain generalized Liénard differential system ⋮ Global analysis of a Liénard system with quadratic damping ⋮ Center conditions for nilpotent cubic systems using the Cherkas method ⋮ Simplified Liénard equation by homotopy analysis method ⋮ Integrability conditions of a resonant saddle in Liénard-like complex systems ⋮ A class of exact solutions of the Liénard-type ordinary nonlinear differential equation ⋮ Generalized Weierstrass integrability for the complex differential equations \(\frac{dy}{dx}=a(x)y^4+b(x)y^3+c(x)y^2+d(x)y+e(x)\) ⋮ Puiseux integrability of differential equations

Cites Work

• On general algebraic mechanisms for producing centers in polynomial differential systems
• Liénard and Riccati differential equations related via Lie algebras
• Weierstrass integrability of differential equations
• An algebraic approach to the classification of centers in polynomial Liénard systems
• Center problem for several differential equations via Cherkas' method
• On the integrability of two-dimensional flows
• Generalized cofactors and nonlinear superposition principles
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• On the differentiability of first integrals of two dimensional flows
• On the local analytic integrability at the singular point of a class of Liénard analytic differential systems
• Limit cycles of the generalized polynomial Liénard differential equations
• Classification of Continuous Flows on 2-Manifolds
• Local analytic integrability for nilpotent centers
• Probleme General de la Stabilite du Mouvement. (AM-17)
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