A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations
Open Access
- 1 April 1978
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 238, 139-164
- https://doi.org/10.2307/1997801
Abstract
We prove a result concerning the global nature of the set of periodic solutions of certain retarded functional differential equations. Our main theorem is an analogue, for retarded F.D.E.'s, of a result by J. Alexander and J. Yorke for ordinary differential equations.Keywords
This publication has 16 references indexed in Scilit:
- The Fuller index and global Hopf bifurcationJournal of Differential Equations, 1978
- Global Bifurcations of Periodic OrbitsAmerican Journal of Mathematics, 1978
- Bifurcation theory for Fredholm operatorsMemoirs of the American Mathematical Society, 1976
- Ordinary differential equations which yield periodic solutions of differential delay equationsJournal of Mathematical Analysis and Applications, 1974
- Some equations modelling growth processes and gonorrhea epidemicsMathematical Biosciences, 1973
- Periodic solutions of certain Lie´nard equations with delayJournal of Differential Equations, 1972
- A periodicity theorem for autonomous functional differential equationsJournal of Differential Equations, 1969
- An Index of Fixed Point Type for Periodic OrbitsAmerican Journal of Mathematics, 1967
- Functional Analysis and Semi-groups. (Revised Edition) By Einai Hille and Ralph S. Phillips. Pp. xii, 808. $13.80, 1957. Americaj Mathematical Society Colloquium Publications, Vol 31. (American Mathematical Society)The Mathematical Gazette, 1959
- An extension of Tietze’s theoremPacific Journal of Mathematics, 1951