Results 1 to 10 of about 910 (138)

Rational limit cycles of Abel differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2023
We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo, Luis Ángel Calderón, Ignacio Ojeda   +2 more
doaj   +5 more sources

Polynomial Solutions of Equivariant Polynomial Abel Differential Equations [PDF]

Advanced Nonlinear Studies, 2018
Let a⁢(x){a(x)} be non-constant and let bj⁢(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a⁢(x)⁢y˙=b1⁢(x)⁢y+b3⁢(x)⁢y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
doaj   +7 more sources

Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations [PDF]

Entropy, 2022
We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent ...
Elena V. Nikolova
doaj   +2 more sources

Abel fractional differential equations using Variation of parameters method

Ratio Mathematica, 2022
The Variation of Parameters Method (VPM) is utilized throughout the research to identify a numerical model for a nonlinear fractional Abel differential equation (FADE).
Nithya Devi, P. Prakash
doaj   +2 more sources

Generalized symmetries, first integrals, and exact solutions of chains of differential equations [PDF]

Open Communications in Nonlinear Mathematical Physics, 2021
New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied.
C. Muriel, M. C. Nucci
doaj   +1 more source

Rational solutions of Abel differential equations

Journal of Mathematical Analysis and Applications, 2022
19 ...
J.L. Bravo, L.A. Calderón, M. Fernández, I. Ojeda   +3 more
openaire   +2 more sources

A Liouville’s Formula for Systems with Reflection

Mathematics, 2021
In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection.
Santiago Codesido, F. Adrián F. Tojo
doaj   +1 more source

On approximation of functions from the class $L^{\psi}_{\beta, 1}$ by the Abel-Poisson integrals in the integral metric

Karpatsʹkì Matematičnì Publìkacìï, 2022
In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
doaj   +1 more source

The Unique Periodic Solution of Abel’s Differential Equation [PDF]

Journal of Mathematics, 2020
In this paper, the existence of a periodic solution for Abel’s differential equation is obtained first by using the fixed-point theorem. Then, by constructing the Lyapunov function, the uniqueness and stability of the periodic solution of the equation are obtained.
openaire   +2 more sources

Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

Advances in Mathematical Physics, 2022
The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy.
Xiaohong Chen
doaj   +1 more source