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Resultats globals: 9 registres trobats en 0.03 segons.
Articles, 9 registres trobats
Articles 9 registres trobats  
1.
18 p, 333.3 KB Solving polynomials with ordinary differential equations / Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours. Institut Denis Poisson)
In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). [...]
2021 - 10.1016/j.exmath.2021.06.001
Expositiones Mathematicae, Vol. 39, Issue 4 (December 2021) , p. 624-643  
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2.
14 p, 670.7 KB Rational limit cycles of Abel equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))
In this paper we deal with Abel equations dy/dx = A(x)y2 + B(x)y3, where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most three rational limit cycles and we characterize when this happens. [...]
2021 - 10.3934/CPAA.2021007
Communications on pure & applied analysis, Vol. 20, Issue 3 (March 2021) , p. 1077-1089  
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3.
23 p, 412.0 KB On the number of limit cycles in generalized abel equations / Huang, Jianfeng (Jinan University. Department of Mathematics (China)) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)
Given p, q ∊ Z ≥ 2 with p ≠ q, we study generalized Abel differential equations (Equation presented), where A and B are trigonometric polynomials of degrees n, m ≥ 1, respectively, and we are interested in the number of limit cycles (i. [...]
2020 - 10.1137/20M1340083
SIAM Journal on Applied Dynamical Systems, Vol. 19, Issue 4 (2020) , p. 2343-2370  
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4.
10 p, 277.6 KB Chini equations and isochronous centers in three-dimensional differential systems / Chamberland, Marc (Grinnell College. Department of Mathematics and Statistics (USA)) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We study the number of limit cycles of T -periodic Chini equations and some generalized Abel equations and apply the results obtained to illustrate the existence of isochronous centers in three-dimensional autonomous differential systems.
2010 - 10.1007/s12346-010-0019-4
Qualitative theory of dynamical systems, Vol. 9, Issue 1-2 (November 2010) , p. 29-38  
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5.
25 p, 744.8 KB Differential equations with a given set of solutions / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ramírez, Rafael Orlando (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Sadovskaia, Natalia (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II)
The aim of this paper is to study the following inverse problem of ordinary differential equations: For a given set of analytic functions ω={z(t),…,z(t)}, with z(t)=x(t)+iy(t) and z¯(t)=x(t)−iy(t) for j=1,…,r, defined in the open interval I⊆R, we want to determine the differential equation F(t,z¯,z,z˙,z¯˙,…,z,z¯)=0,where [Formula presented] for j=1,…,n, in such a way that the given set of functions ω is a set of solutions of this differential equation.
2020 - 10.1016/j.amc.2019.124659
Applied Mathematics and Computation, Vol. 365 (January 2020) , art. 124659  
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6.
7 p, 678.5 KB Polynomial solutions of equivariant polynomial Abel differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
Let a(x) be non-constant and let bj(x), for 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 = b(x)y + b(x)y, with b(x) =/ 0, and the real or complex polynomial equivariant polynomial Abel differential equation of the second kind a(x)yy = b0(x) + b(x)y, with b(x) =/ 0, have at most 7 polynomial solutions. [...]
2018 - 10.1515/ans-2017-6043
Advanced Nonlinear Studies, Vol. 18, Issue 3 (August 2018) , p. 537-542  
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7.
6 p, 305.1 KB Centers of planar generalized Abel equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques.) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We deal with the differential equation ̇r=dr/dθ=a(θ)rn+b(θ)rm, where (r,θ) are the polar coordinates in the plane R2, m and n are integers such that m > n ≥ 2, and a,b are C1 functions. Note that when n=2 and m=3 we have an Abel differential equation. [...]
2020 - 10.1016/j.jde.2019.11.046
Journal of differential equations, Vol. 268, Issue 10 (May 2020) , p. 6481-6487  
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8.
17 p, 389.6 KB Periodic solutions of linear, Riccati, and Abel dynamic equations / Bohner, Martin (Missouri S&T) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)
We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. [...]
2019 - 10.1016/j.jmaa.2018.10.018
Journal of mathematical analysis and applications, Vol. 470, Núm. 2 (February 2019) , p. 733-749  
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9.
11 p, 683.1 KB Generalized Weierstrass integrability of the Abel differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
We study the Abel differential equations that admits either a generalized Weierstrass first integral or a generalized Weierstrass inverse integrating factor.
2013 - 10.1007/s00009-013-0266-0
Mediterranean Journal of Mathematics, Vol. 10 Núm. 4 (2013) , p. 1749-1760  
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