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On the null spaces of linear Fredholm operators depending on several parameters

Published online by Cambridge University Press:  24 October 2008

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

Let X, Y be real Banach spaces, and let = {f(λ):λ ∈ m} be an m-parameter family of bounded linear operators from X to Y, with f(λ) depending continuously on λ. The cases m = 1 and m = 2 are considered, and conditions on are found which determine the null space of f(λ) for all λ near a given λ0 such that f(λ0): X → Y is a Fredholm operator. The results obtained are shown to be of particular interest in perturbed bifurcation theory.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 131 - 142
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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