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-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.
Original language | English (US) |
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Pages (from-to) | 191-222 |
Number of pages | 32 |
Journal | Zeitschrift fur Angewandte Mathematik und Physik |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2011 |
Keywords
- Age structured model
- Cauchy problem
- Functional differential equation
- Hopf bifurcation
- Non-dense domain
- Periodic solution
ASJC Scopus subject areas
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics