Abel-like differential equations with no periodic solutions

DOI10.1016/j.jmaa.2007.12.060zbMath1357.34074OpenAlexW2012948976MaRDI QIDQ2481899

Joan Torregrosa, J. L. Bravo

Publication date: 15 April 2008

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.2007.12.060

zbMATH Keywords

periodic solutionslimit cyclesAbel equationHilbert's 16th problemrigid systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25)

Related Items (17)

Uniqueness of limit cycles for polynomial first-order differential equations ⋮ Uniqueness of limit cycles for quadratic vector fields ⋮ LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS ⋮ Centers and limit cycles for a family of Abel equations ⋮ 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 ⋮ Stability of singular limit cycles for Abel equations revisited ⋮ Hilbert number for a family of piecewise nonautonomous equations ⋮ Limit cycles of Abel equations of the first kind ⋮ Characterization of the existence of non-trivial limit cycles for generalized Abel equations ⋮ Stability of singular limit cycles for Abel equations ⋮ Abel-like differential equations with a unique limit cycle ⋮ Periodic solutions with nonconstant sign in Abel equations of the second kind ⋮ Alien limit cycles in Abel equations ⋮ A geometric criterion for equation \(\dot{x} = \sum\nolimits_{i = 0}^m a_i(t) x^i\) having at most \(m\) isolated periodic solutions

Cites Work

• Existence of closed solutions for a polynomial first order differential equation
• A new uniqueness criterion for the number of periodic orbits of Abel equations
• Periodic solutions of Abel differential 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 \(x(0)=x(1)\)
• Cubic systems and Abel equations
• Limit cycles for rigid cubic systems
• The number of periodic solutions of polynomial differential equations
• Limit Cycles for a Class of Abel Equations
• Limit cycles of a class of polynomial systems
• Periodic solutions of polynomial first order differential equations
• Exact number of limit cycles for a family of rigid systems
• LIMIT CYCLES FOR GENERALIZED ABEL EQUATIONS
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