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Hopf bifurcation for non-densely defined Cauchy problems |
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| Authors: | Zhihua Liu Pierre Magal Shigui Ruan |
| Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People??s Republic of China 2. UMR CNRS 5251, IMB& INRIA sud-ouest Anubis, Universit?? de Bordeaux, 146 rue L??o Saignat, 33076, Bordeaux, France 3. Department of Mathematics, University of Miami, Coral Gables, FL, 33124-4250, USA |
| Abstract: | 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?CYosida 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. |
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