Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-13T19:55:37.905Z Has data issue: false hasContentIssue false
  • English
  • Français

An example of “secondary bifurcation” in a non-autonomous two-point boundary value problem

Published online by Cambridge University Press:  14 November 2011

Ph. Clément  and
J. vanKan
Ph. Clément
Affiliation:
University of Technology, Department of Mathematics, Julianalaan 132, 2628 BL Delft, The Netherlands
J. vanKan
Affiliation:
University of Technology, Department of Mathematics, Julianalaan 132, 2628 BL Delft, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Synopsis

We consider the continuation of positive solutions of -u" = λs(x)f(u), with appropriate boundary conditions and with positive s and f. We show by an example that bifurcation may occur from the curve of these positive solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 101 - 105
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Amann, H.. Nonlinear eigenvalue problems having precisely two solutions. Math. Z. 150 (1976), 27–37.Google Scholar
2Clemént, Ph. and Peletier, L. A.. On positive, concave solutions of two point nonlinear eigenvalue problems. J. Math. Anal. Appl 69 (1979), 329è340.Google Scholar
3Crandall, M. G. and Rabinowitz, P. H.. Bifurcation, perturbation of simple eigenvalues, and linearized stability. Arch. Rational Mech. Anal. 52 (1973), 161–180.Google Scholar
4Gelfand, I. M.. Some problems in the theory of quasilinear equations. Trans. Amer. Math. Soc. 29 (1963), 295–381.Google Scholar
5Laetsch, T.. Critical solutions of autonomous nonlinear boundary value problems. Indiana Univ. Math. J. 24 (1975), 651–658.CrossRefGoogle Scholar
6McLeod, J. B. and Stuart, C. A.. Non-linear Sturm-Liouville problems with no secondary bifurcation. Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 347–356.Google Scholar
7Rabinowitz, P. H.. A note on a nonlinear eigenvalue problem for a class of differentialequations. J. Differential Equations 9 (1971), 536–548.CrossRefGoogle Scholar
8Rabinowitz, P. H.. Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. Math. 3 (1973), 161–202.Google Scholar