Abel-like differential equations with no periodic solutions
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Publication:2481899
DOI10.1016/j.jmaa.2007.12.060zbMath1357.34074OpenAlexW2012948976MaRDI QIDQ2481899
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
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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