Results 11 to 20 of about 36,931 (242)
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
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Relativistic dissipative cosmological models and abel differential equation
Computers & Mathematics with Applications, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mak, MK, Harko, T
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Periodic solutions of Abel differential equations
Journal of Mathematical Analysis and Applications, 2007 For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.
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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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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 $\mathcal E_\Gamma$ of Abel differential equations $\frac{dv}{dt}=a_1 v^2+a_2 v^3$, $a_1,a_2\in L^\infty ([0,T])$, such that images of Lipschitz paths $\tilde A:=\bigl(\int_0^\cdot a_1(s)ds, \int_0^\cdot a_2(s)ds\
Brudnyi, Alexander
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Homotopy analysis method for solving Abel differential equation of fractional order
Open Physics, 2013 Jafari Hossein +3 more
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Rational solutions of Abel differential equations
Journal of Mathematical Analysis and Applications, 2022 19 ...
J.L. Bravo +3 more
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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 +2 more
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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.
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Generalized Weierstrass Integrability of the Abel Differential Equations
Mediterranean Journal of Mathematics, 2013 We study the Abel differential equations that admits either a generalized Weierstrass first integral or a generalized Weierstrass inverse integrating factor.
Llibre, Jaume, Valls, Clàudia
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