Results 41 to 50 of about 930 (158)

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, Maite Grau, Xavier Santallusia   +2 more
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Abel-like differential equations with no periodic solutions

Journal of Mathematical Analysis and Applications, 2008
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Bravo, J.L., Torregrosa, J.
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Fractional Abel Differential Equation Application in Edge Detection: FADEED

Journal of Image Processing and Artificial Intelligence, 2023
There is a long history of perturbed implementations of Abel differential equations in dynamics, linear systems with stochasticity, modeling approaches, and linear algebra. Numerous research has been undertaken, the bulk of which have focused on Abel differential equation techniques and the use of the Abel differential equation using the variation ...
N. Nithyadevi, P. Prakash
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Abel differential equations admitting a certain first integral

Journal of Mathematical Analysis and Applications, 2010
Abel differential equations in the form \[ \frac{dy}{dx}=a(x)y^3+b(x)y^2+c(x)y+d(x) \] are investigated in the present work. Conditions to have a certain first integral are given and these conditions establishing a bridge with Galois theory. The paper ends with two examples.
Giné, Jaume, Santallusia, Xavier
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Corrigendum: On the Abel differential equations of third kind

Discrete & Continuous Dynamical Systems - B, 2022
<p style='text-indent:20px;'>In this paper, using the Poincaré compactification technique we classify the topological phase portraits of a special kind of quadratic differential system, the Abel quadratic equations of third kind. In [<xref ref-type="bibr" rid="b1">1</xref>] where such investigation was presented for the first time ...
Regilene Oliveira, Cláudia Valls
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Universal curves in the center problem for Abel differential equations [PDF]

Ergodic Theory and Dynamical Systems, 2014
We study the center problem for the class ${\mathcal{E}}_{{\rm\Gamma}}$ of Abel differential equations $dv/dt=a_{1}v^{2}+a_{2}v^{3}$, $a_{1},a_{2}\in L^{\infty }([0,T])$, such that images of Lipschitz paths $\tilde{A}:=(\int _{0}^{\cdot }a_{1}(s)\,ds,\int _{0}^{\cdot }a_{2}(s)\,ds):[0,T]\rightarrow \mathbb{R}^{2}$ belong to a fixed compact rectifiable ...
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Algebraic geometry of the center-focus problem for Abel differential equations [PDF]

Ergodic Theory and Dynamical Systems, 2014
The Abel differential equation $y^{\prime }=p(x)y^{3}+q(x)y^{2}$ with polynomial coefficients $p,q$ is said to have a center on $[a,b]$ if all its solutions, with the initial value $y(a)$ small enough, satisfy the condition $y(a)=y(b)$. The problem of giving conditions on $(p,q,a,b)$ implying a center for the Abel equation is analogous to the classical
Briskin, M., Pakovich, F., Yomdin, Y.
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General Solutions of the Abel Differential Equations

, 2020
The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind. A novel derivative condition for the general solution of first-kind Abel equation is introduced.
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Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations [PDF]

Physics Letters A, 2013
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative ...
Mancas, Stefan C., Rosu, Haret C.
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New numerical method based on Generalized Bessel function to solve nonlinear Abel fractional differential equation of the first kind

Nonlinear Engineering, 2019
Fractional calculus and fractional differential equations (FDE) have many applications in different branches of sciences. But, often a real nonlinear FDE has not the exact or analytical solution and must be solved numerically.
Parand K., Nikarya M.
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