Hopf bifurcation calculations for functional differential equations. (English) Zbl 0592.34048

The author presents an alternate method for analyzing the Hopf bifurcation problem in a class of functional differential equations with unbounded delay: \(\dot y(t)=\int^{0}_{\infty}d\eta (\alpha;s)y_ t(s)+H(\alpha;y_ t).\) An advantage of this method over previous ones for example by S.-N. Chow and J. Mallet-Paret [J. Differ. Equations 26, 112-159 (1977; Zbl 0367.34033)] is that it avoids all reference to the infinite-dimensional nature of the problem. Its importance lies both in its generality and its relative ease of applications. The method is based on Lyapunov-Schmidt means and is motivated by the work of J. C. De Oliveira and J. K. Hale [Tôhoku Math. J., II. Ser. 32, 577-592 (1980; Zbl 0454.34035)].
Reviewer: Jing Huang Tian


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
Full Text: DOI


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