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Bifurcation from Eigenvalues in Non-Linear Multiparameter Sturm-Liouville Problems

Published online by Cambridge University Press:  18 May 2009

Patrick J. Browne  and
B. D. Sleeman
Patrick J. Browne
Affiliation:
Department of Mathematics, University of Calgary, Alberta T2N 1N4, Canada
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland
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This paper continues our study of non-linear multiparameter eigenvalue problems. In recent work [3], [4], [5] we have discussed bifurcation from eigenvalues in both abstract and concrete multiparameter problems. In this note we present further simple conditions which will ensure bifurcation from eigenvalues of a multiparameter Sturm-Liouville problem. We consider the regular case and the asymptotic case of bifurcation from infinity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 85 - 90
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Atkinson, F. V., Multiparameter eigenvalue problems, Vol I: Matrices and compact operators (Academic Press, 1972).Google Scholar
2.Binding, P. A. and Browne, P. J., Positivity results for determinantal operators, Proc. Roy. Soc. Edinburgh Sect A, 81 (1978), 267–271.Google Scholar
3.Browne, P. J. and Sleeman, B. D., Non-linear multiparameter eigenvalue problems for ordinary differential equations, submitted.Google Scholar
4.Browne, P. J. and Sleeman, B. D., Non-linear multiparameter Sturm-Liouville problems, J. Differential Equations (to appear).Google Scholar
5.Browne, P. J. and Sleeman, B. D., Non-linear multiparameter eigenvalue problems, J. Nonlinear Analysis (to appear).Google Scholar
6.Rabinowitz, P. H., Non-linear Sturm-Liouville problems for second order ordinary differential equations, Comm. Pure Appl. Math. 23 (1970), 939–961.Google Scholar
7.Sleeman, B. D., Multiparameter spectral theory in Hilbert space, Research notes in Mathematics (Pitman Press, London, 1978).Google Scholar
8.Stuart, C. A., Solutions of large norm for non-linear Sturm–Liouville problems, Quart. J. Math. Oxford Ser 2, 24 (1973), 129–139.Google Scholar
9.Toland, J. F., Asymptotic linearity and nonlinear eigenvalue problems, Quart. J. Math. Oxford Ser. 2, 24 (1973), 241–250.Google Scholar
10.Turner, R. E. L., Superlinear Sturm-Liouville problems, J. Differential Equations 13 (1973) 157–171.Google Scholar