ON SMITH,R.A. AUTONOMOUS CONVERGENCE THEOREM

被引：104

作者：

LI, MY

MULDOWNEY, JS

机构：

[1] GEORGIA INST TECHNOL,CTR DYNAM SYST & NONLINEAR STUDIES,ATLANTA,GA 30332

[2] UNIV ALBERTA,DEPT MATH,EDMONTON,AB T6G 2G1,CANADA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 1995年 / 25卷 / 01期

关键词：

D O I：

10.1216/rmjm/1181072289

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

R.A. Smith [19] showed that his higher dimensional generalization of Bendixson's criterion for the nonexistence of periodic solutions to an autonomous differential equation implies that all bounded trajectories tend to an equilibrium. Here it is shown that a similar conclusion can be drawn from a generalized Dulac criterion. These conditions are also shown to have strong implications for the structure of invariant sets.

引用

页码：365 / 379

页数：15

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