Existence of periodic orbits for high-dimensional autonomous systems

被引：22

作者：

Sanchez, Luis A. ^{[1
]}

机构：

[1] Univ Politecn Cartagena, Dept Matemat Aplicada & Estadist, Escuela Univ Ingn Tecn Civil, Murcia 30203, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 363卷 / 02期

关键词：

Periodic orbits; Poincare-Bendixson property; Autonomous systems;

D O I：

10.1016/j.jmaa.2009.08.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension. It is based on a Poincare-Bendixson property enjoyed by a new class of monotone systems introduced in [L.A. Sanchez, Cones of rank 2 and the Poincare-Bendixson property for a new class of monotone systems, J. Differential Equations 216 (2009) 1170-1190]. A concrete application is done to a scalar differential equation of order 4. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：409 / 418

页数：10

共 18 条

[1] PERSISTENCE IN DYNAMIC-SYSTEMS [J].

BUTLER, G ;

WALTMAN, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1986, 63 (02) :255-263

[2]

Chicone C, 1999, texts in applied mathematics, V34

[3] A generalization of Bendixson's criterion [J].

Feckan, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (11) :3395-3399

[4] Criteria on the nonexistence of invariant Lipschitz submanifolds for dynamical systems [J].

Feckan, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 174 (02) :392-419

[5]

FECKAN M, 2000, NONLINEAR OSCIL N Y, V3, P271

[6] A PERRON THEOREM FOR THE EXISTENCE OF INVARIANT SUBSPACES [J].

FUSCO, G ;

OLIVA, WM .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1991, 160 :63-76

[7]

Hartman P., 1980, ORDINARY DIFFERENTIA

[8]

Hirsch MW, 2005, HBK DIFF EQUAT ORDIN, V2, P239

[9]

Krasnoselskij MA., 1989, Positive linear systems: the method of positive operators

[10]

Krasnoselskij MA, 1984, GEOMETRICAL METHODS

← 1 2 →