Results 11 to 20 of about 13,396 (146)
On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations
Journal of Differential Equations, 2017 In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions.
A. Cima, A. Gasull, F. Mañosas
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Uniqueness of limit cycles for quadratic vector fields [PDF]
, 2019 Producción CientíficaThis article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x ′ = a1x − y − a3x 2 + (2a2 + a5)xy+a6y 2 , y ′ = x ...
Bravo, José Luis +3 more
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Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials [PDF]
Nonlinearity, 2009 A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic ...
Cariñena, José F. +2 more
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A Chiellini type integrability condition for the generalized first kind Abel differential equation [PDF]
, 2013 The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}$, where $\alpha \in \Re$, and ...
Harko, Tiberiu +2 more
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Bernstein Polynomials For Solving Abels Integral Equation
Journal of Mathematics and Computer Science, 2011 This paper presents a numerical method for solving Abel’s integral equation as singular Volterra integral equations. In the proposed method, the functions in Abel’s integral equation are approximated based on Bernstein polynomials (BPs) and therefore, the solving of Abel’s integral equation is reduced to the solving of linear algebraic equations ...
Mohsen Alipour, Davood Rostamy
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On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation [PDF]
, 2014 We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of integrations on each
Pietrzkowski, Gabriel
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Computing Linear Matrix Representations of Helton-Vinnikov Curves [PDF]
, 2012 Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We
A Beauville +18 more
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Universal centers in the cubic trigonometric Abel equation
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We study the center problem for the trigonometric Abel equation $d \rho/ d \theta= a_1 (\theta) \rho^2 + a_2(\theta) \rho^3,$ where $a_1(\theta)$ and $a_2(\theta)$ are cubic trigonometric polynomials in $\theta$.
Jaume Giné +2 more
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Zero distribution of polynomials satisfying a differential-difference equation [PDF]
, 2013 In this paper we investigate the asymptotic distribution of the zeros of polynomials $P_{n}(x)$ satisfying a first order differential-difference equation.
Dominici, Diego, Van Assche, Walter
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A counterexample to the composition condition conjecture for polynomial Abel differential equations [PDF]
Ergodic Theory and Dynamical Systems, 2018 Polynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works pointed out that all centers of the polynomial Abel differential equations satisfied the composition conditions (also called ...
JAUME GINÉ +2 more
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