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Non-linear Sturm-Liouville problems with no secondary bifurcation†

Published online by Cambridge University Press:  14 November 2011

J. B. McLeod  and
C. A. Stuart
J. B. McLeod
Affiliation:
Wadham College, Oxford
C. A. Stuart
Affiliation:
Département de mathématiques, École Polytechnique Fédérale de Lausanne
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Synopsis

The paper is concerned with giving sufficient conditions that in the non-linear boundary-value problem

there should be no secondary bifurcation, i.e. that, given a branch of solutions (u, λ) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 3-4 , 1978 , pp. 347 - 356
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

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