Rational Periodic Solutions on Some Generalized Abel Equations

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Cites Work

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Existence of non-trivial limit cycles in Abel equations with symmetries
Limit cycles of Abel equations of the first kind
Stability of singular limit cycles for Abel equations
On the polynomial limit cycles of polynomial differential equations
On the rational limit cycles of Abel equations
Existence of closed solutions for a polynomial first order differential equation
Iterative approximation of limit cycles for a class of Abel equations
The number of limit cycles for generalized Abel equations with periodic coefficients of definite sign
On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
Alien limit cycles in Abel equations
Rational limit cycles of Abel equations
Rational solutions of Abel differential equations
Rational solutions of Abel trigonometric polynomial differential equations
Centers and limit cycles for a family of Abel equations
Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves
Lower bounds for the number of limit cycles of trigonometric Abel equations
Integrability and limit cycles for Abel equations
Limit Cycles for a Class of Abel Equations
A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions
LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS
Rational limit cycles on generalized Bernouilli polynomial equations

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