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Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

Published online by Cambridge University Press:  20 January 2009

A. J. B. Potter
A. J. B. Potter
Affiliation:
University of Aberdeen, Aberdeen AB9 2TY, Scotland
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In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 299 - 308
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1.Browder, F. E. and Petryshyn, W. V., Approximation methods and the generalised topological degree for non-linear mappings in Banach space, J. Fund. Anal. 3 (1968), 217–245.CrossRefGoogle Scholar
2.Chow, S. N. and Mallet-Paret, J., The Fuller index and global Hopf bifurcation, J. Differential Equations 39 (1978), 66–84.Google Scholar
3.Fuller, F. B., An index of fixed point type for periodic orbits, Amer. J. Math. 89 (1967), 133–148.Google Scholar
4.Nussbaum, R. D. and Potter, A. J. B., Cyclic differential equations and period three solutions of differential-delay equations, J. Differential Equations 46 (1982), 379–408.Google Scholar
5.Potter, A. J. B., On a generalisation of the Fuller index, Proceedings of the 1983 AMS Summer Institute on non-linear functional analysis and applications, to appear.Google Scholar