An improvement to Darboux integrability theorem for systems having a center

被引：7

作者：

Chavarriga, J

Giacomini, H

Giné, J

机构：

[1] Univ Lleida, Dept Matemat, Lleida 25001, Spain

[2] Univ Tours, Fac Sci & Tech, Lab Math & Phys Theor, F-37200 Tours, France

来源：

APPLIED MATHEMATICS LETTERS | 1999年 / 12卷 / 08期

关键词：

nonlinear differential equations; integrability; center problem;

D O I：

10.1016/S0893-9659(99)00127-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider planar polynomial differential systems of degree m with a center at the origin and with an arbitrary linear part. We show that if the system has m(m + 1)/2 - [(m + 1)/2] algebraic solutions or exponential factors then it has a Darboux integrating factor. This result is an improvement of the classical Darboux integrability theorem and other recent results about integrability. (C) 1999 Elsevier Science Ltd. All rights reserved.

引用

页码：85 / 89

页数：5

共 14 条

[1]

CAIRO L, UNPUB P ROYAL LONDON

[2]

CHAVARRIGA J, 1997, EXPO MATH, V15, P161

[3] INVARIANT ALGEBRAIC-CURVES AND CONDITIONS FOR A CENTER [J].

CHRISTOPHER, CJ .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 :1209-1229

[4]

Cozma D, 1995, NODEA-NONLINEAR DIFF, V2, P21

[5]

Darboux G., 1878, B SCI MATH, V2, P60

[6]

DARBOUX G, 1878, B SCI MATH ASTRON, V2, P123

[7]

Darboux G., 1878, B SCI MATH, V2, P151

[8]

GASULL A, 1993, EQ 91 INT C DIFF EQ, V2, P531

[9]

Hilbert D., 1900, Nachrichten Ges. Wiss. Gott, V1900, P253

[10]

Jouanolou J.P., 1979, LECT NOTES MATH, V708

← 1 2 →