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Articles, 5 registres trobats
Articles 5 registres trobats  
1.
7 p, 977.8 KB Rational first integrals of the Liénard equations : The solution to the Poincaré problem for the Liénard equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Pessoa, Claudio (Universidade Estadual Paulista. Departamento de Matemática) ; Ribeiro, Jarne D. (Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais)
Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations ẍ + f (x)ẋ + x = 0, being f (x) a polynomial of arbitrary degree. [...]
2021 - 10.1590/0001-3765202120191139
Anais da Academia Brasileira de Ciencias, Vol. 93, Issue 4 (2021) , p. e20191139
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2.
32 p, 490.7 KB On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory / Acosta-Humánez, Primitivo B. (Universidad del Atlántico and Intelectual.Co. Department of Mathematics (Colombia)) ; Lázaro, J. Tomás (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I) ; Morales Ruiz, Juan J. (Universidad Politécnica de Madrid. Departamento de Matemática Aplicada) ; Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Liénard equations and equations related with special functions such as Hypergeometric and Heun ones. [...]
2015 - 10.3934/dcds.2015.35.1767
Discrete and continuous dynamical systems. Series A, Vol. 35, Issue 5 (May 2015) , p. 1767-1800  
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3.
10 p, 300.3 KB Periodic solutions of Lienard differential equations via averaging theory of order two / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
For ε = 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x + f(x)x + n2x + g(x) = ε2p1(t) + ε3p2(t), where n is a positive integer, f : R → R is a C3 function, g : R → R is a C4 function, and pi : R → R for i = 1, 2 are continuous 2π-periodic function. [...]
2015 - 10.1590/0001-3765201520140129
Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 4 (2015) , p. 1905-1913  
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4.
19 p, 720.6 KB On the maximum number of limit cycles of a class of generalized Liénard differential systems / Alavez-Ramírez, Justino (UJAT(México). Division Académica de Ciencias Básicas) ; Blé, Gamaliel (UJAT(México). Division Académica de Ciencias Básicas) ; López-López, Jorge (UJAT(México). Division Académica de Ciencias Básicas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Applying the averaging theory of first, second and third order to one class generalized polynomial Li'enard differential equations, we improve the known lower bounds for the maximum number of limit cycles that this class can exhibit.
2012 - 10.1142/S0218127412500630
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 22 Núm. 3 (2012) , p. 1250063  
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5.
18 p, 797.8 KB Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)
We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations x = y + sgn(gm (x, y))F (x), y = −x, where the zero set of the function sgn(gm (x, y)) with m = 2, 4, 6, . [...]
2015 - 10.1007/s00033-013-0393-2
ZAMP. Journal of Applied Mathematics and Physics, Vol. 66 Núm. 1 (2015) , p. 51-66  
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