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Small solutions of a non-linear equation in Banach space for a degenerate case

Published online by Cambridge University Press:  14 February 2012

M. Shearer
M. Shearer
Affiliation:
Fluid Mechanics Research Institute, University of Essex
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Synopsis

The existence of zeroes of an operator in Banach space near a. known zero is examined, when the non-degeneracy condition of Magnus [1] is violated, and replaced by a condition which is called simple-degeneracy. Criteria are given which help determine the number and the structure of curves of zeroes of the operator, passing through the known zero.

These conditions and results are interpreted in terms of bifurcation theory. By considering several different cases, it is shown that the failure of various conditions frequently employed in the Lyapunov–Schmidt method may be overcome using the idea of simple-degeneracy.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 35 - 49
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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