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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

1Crandall, M. G. and Rabinowitz, P. H.Bifurcation from simple eigenvalues. J. Functional Anal. 8 (1971), 321–340.CrossRefGoogle Scholar
2Laetsch, T.Critical solutions of autonomous non-linear boundary value problems. Indiana Univ. Math. J. 24 (1975), 651–658.CrossRefGoogle Scholar
3Bazley, N. W. and Pimbley, G. H.A region of no secondary bifurcation for non-linear Hammerstein operators. Z. Angew. Math. Phys. 25 (1974), 743–751.CrossRefGoogle Scholar
4Coffman, C. V.On the uniqueness of solutions of a non-linear boundary value problem. J. Math. Mech. 13 (1964), 751–763.Google Scholar
5Kolodner, I.I.Heavy rotating string—a non-linear eigenvalue problem. Comm. Pure Appl. Math. 8 (1955), 395–408.CrossRefGoogle Scholar