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Rational Limit Cycles on Abel Polynomial Equations
Mathematics, 2020 In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 . We prove that these Abel equations can have at most two rational (
Claudia Valls
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Parametric Centers for Trigonometric Abel Equations
Journal of Dynamics and Differential Equations, 2008Jean-Pierre Françoise
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Physica Scripta, 2023
In this paper, the concept of the trigonometric representation of parameterized interval analysis is introduced to investigate a theory of the interval-valued Abel integral equation (IAIE) on a time scale.
Lai van Phut, Ngo van Hoa
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In this paper, the concept of the trigonometric representation of parameterized interval analysis is introduced to investigate a theory of the interval-valued Abel integral equation (IAIE) on a time scale.
Lai van Phut, Ngo van Hoa
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The space of solvable Pell–Abel equations
Compositio Mathematica, 2023A Pell–Abel equation is a functional equation of the form $P^{2}-DQ^{2} = 1$ , with a given polynomial $D$ free of squares and unknown polynomials $P$ and $Q$ .
Andrei Bogatyrëv, Q. Gendron
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Journal of Differential Equations, 2023
This paper devotes to the study of the classical Abel equation $\frac{dx}{dt}=g(t)x^{3}+f(t)x^{2}$, where $g(t)$ and $f(t)$ are trigonometric polynomials of degree $m\geq1$. We are interested in the problem that whether there is a uniform upper bound for
Xiangqin Yu +2 more
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This paper devotes to the study of the classical Abel equation $\frac{dx}{dt}=g(t)x^{3}+f(t)x^{2}$, where $g(t)$ and $f(t)$ are trigonometric polynomials of degree $m\geq1$. We are interested in the problem that whether there is a uniform upper bound for
Xiangqin Yu +2 more
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On the Number of Limit Cycles in Generalized Abel Equations
SIAM Journal on Applied Dynamical Systems, 2020 Given $p,q\in\mathbb{Z}_{\geq 2}$ with $p\neq q$, we study generalized Abel differential equations $\frac{dx}{d\theta}=A(\theta)x^p+B(\theta)x^q,$ where $A$ and $B$ are trigonometric polynomials of...
Jianfeng Huang +2 more
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On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations
Journal of Differential Equations, 2017 Armengol Gasull, Francesc Mañosas
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Rational Periodic Solutions on Some Generalized Abel Equations
Journal of Dynamical Systems and Geometric Theories, 2022In this paper we deal with the equations a(x)dy/dx = A(x)y 2 + B(x)y 3, where a(x), A(x) and B(x) are complex polynomials with a(x)B(x) ≢ 0 and a(x) non-constant.
C. Valls
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Lower bounds for the number of limit cycles of trigonometric Abel equations
Journal of Mathematical Analysis and Applications, 2008Maria Jesus Alvarez, Armengol Gasull
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Nonlinear Analysis: Real World Applications, 2022
where p, q ∈ Z \{ 1 } , q − 1 p − 1 / ∈ Z ≤ 1 and a p , a q are piecewise trigonometrical polynomials of degree m with two zones 0 ≤ θ < θ 1 and θ 1 ≤ θ ≤ 2 π .
Jianfeng Huang, J. Li
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where p, q ∈ Z \{ 1 } , q − 1 p − 1 / ∈ Z ≤ 1 and a p , a q are piecewise trigonometrical polynomials of degree m with two zones 0 ≤ θ < θ 1 and θ 1 ≤ θ ≤ 2 π .
Jianfeng Huang, J. Li
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