Hopf bifurcation for non-densely defined Cauchy problems

被引：80

作者：

Liu, Zhihua ^{[1
]}

Magal, Pierre ^{[2
,4
]}

Ruan, Shigui ^{[3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Univ Bordeaux, CNRS, IMB, UMR 5251, F-33076 Bordeaux, France

[3] Univ Miami, Dept Math, Coral Gables, FL 33124 USA

[4] Univ Bordeaux, INRIA Sud Ouest Anubis, F-33076 Bordeaux, France

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2011年 / 62卷 / 02期

基金：

美国国家科学基金会;

关键词：

Hopf bifurcation; Cauchy problem; Non-dense domain; Periodic solution; Functional differential equation; Age structured model; TIME-PERIODIC-SOLUTIONS; INTEGRATED SEMIGROUPS; EQUATIONS; STABILITY; THEOREM;

D O I：

10.1007/s00033-010-0088-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille-Yosida operator. The theorem is proved using the center manifold theory for non-densely defined Cauchy problems associated with the integrated semigroup theory. As applications, the main theorem is used to obtain a known Hopf bifurcation result for functional differential equations and a general Hopf bifurcation theorem for age-structured models.

引用

页码：191 / 222

页数：32

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