A note on: "The generalized Lienard polynomial differential systems x′ = y, y′ = -g(x) - f(x)y, with deg g = deg f+1, are not Liouvillian integrable" [Bull. Sci. math. 139 (2015) 214-227]

被引：4

作者：

Gine, Jaume ^{[1
]}

机构：

[1] Univ Lleida, Dept Matemat, Avda Jaume II 69, Lleida 25001, Catalonia, Spain

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2020年 / 161卷

关键词：

Lienard systems; Center problem; Order of a focus; 1ST INTEGRALS;

D O I：

10.1016/j.bulsci.2020.102857

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we give a counterexample to the main result of the work "The generalized Lienard polynomial differential systems x' = y, y' = -g(x) - f(x)y, with deg g = deg f + 1, are not Liouvillian integrable" [Bull. Sci. Math. 139 (2015) 214-227] and give the correct statement of the result. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页数：3

共 6 条

[1]

Christopher C.J., 1999, ELECT J DIFFER EQU, P49

[2]

HAYASHI M, 1996, FUNKC EKVACIOJ-SER I, V39, P403

[3] Liouvillian first integrals for a class of generalized Lienard polynomial differential systems [J].

Llibre, Jaume ;

Valls, Claudia .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (06) :1195-1210

[4] Liouvillian Integrability Versus Darboux Polynomials [J].

Llibre, Jaume ;

Valls, Claudia ;

Zhang, Xiang .

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2016, 15 (02) :503-515

[5] The generalized Lienard polynomial differential systems x′ = y, y′ = -g(x) - f (x)y with deg g = deg f+1 are not Liouvillian integrable [J].

Llibre, Jaume ;

Valls, Claudia .

BULLETIN DES SCIENCES MATHEMATIQUES, 2015, 139 (02) :214-227

[6] LIOUVILLIAN 1ST INTEGRALS OF DIFFERENTIAL-EQUATIONS [J].

SINGER, MF .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 333 (02) :673-688

← 1 →