Existence of closed solutions for a polynomial first order differential equation

DOI10.1016/j.jmaa.2006.05.078zbMath1115.34038OpenAlexW2091050507WikidataQ115346269 ScholiaQ115346269MaRDI QIDQ864627

Pedro J. Torres

Publication date: 12 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.05.078

zbMATH Keywords

limit cycleplanar polynomial vector fieldclosed solutionabel equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (11)

Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Existence of solutions of a new class of impulsive initial value problems of singular nonlinear fractional differential systems ⋮ Solvability of anti-periodic BVPs for impulsive fractional differential systems involving Caputo and Riemann-Liouville fractional derivatives ⋮ Rational solutions of Abel trigonometric polynomial differential equations ⋮ Uniformly attracting solutions of nonautonomous differential equations ⋮ Abel-like differential equations with no periodic solutions ⋮ Periodic solutions with nonconstant sign in Abel equations of the second kind ⋮ Rational limit cycles of Abel equations ⋮ Rational limit cycles on Bernoulli and Riccati equations ⋮ Rational limit cycles on generalized Bernouilli polynomial equations

Cites Work

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• Existence and monotone method for periodic solutions of first-order differential equations
• A generalized upper and lower solutions method and multiplicity results for nonlinear first-order ordinary differential equations
• Cubic systems and Abel equations
• Existence of closed solutions of an equation \(\dot x=f(t,x)\), where \(f_x'(t,x)\) is weakly convex or concave in \(x\)
• Morin singularities and global geometry in a class of ordinary differential operators
• Limit cycles for rigid cubic systems
• Limit Cycles for a Class of Abel Equations
• Old and New Results for First Order Periodic ODEs without Uniqueness: a Comprehensive Study by Lower and Upper Solutions
• Exact number of limit cycles for a family of rigid systems
• LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS

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