Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T08:42:13.036Z Has data issue: false hasContentIssue false
  • English
  • Français

An estimate on the eigenvalues in bifurcation for gradient mappings

Published online by Cambridge University Press:  18 May 2009

Raffaele Chiappinelli
Raffaele Chiappinelli
Affiliation:
Dipartimento di Matematica, Universitá di Siena, 53100 Siena (Italy), E-mail: chiappinelli@unisi.it
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let H be a real Hilbert space and let A: H→H be a nonlinear operator such that A(0) = 0. We consider the eigenvalue problem

Recall that λ0 ε ℝ is said to be a bifurcation point for (1.1) if every neighbourhood of (λ0, 0) in ℝ × H contains solutions of (1.1).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997, pp. 211 - 216
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Amann, H., Liusternik-Schnirelmann theory and nonlinear eigenvalue problems, Math. Ann. 199 (1972), 55–72.CrossRefGoogle Scholar
2.Berger, M. S., Nonlinearity and functional analysis (Academic Press, New York, 1977).Google Scholar
3.Brezis, H., Analyse fonctionnelle, theorie et applications (Masson, Paris, 1983).Google Scholar
4.De Figueiredo, D. G., Lectures on the Ekeland variational principle with applications and detours (Tata Inst. of Fundamental Research, Bombay, 1989).Google Scholar
5.Dieudonne, J., Foundations of modern analysis (Academic Press, New York, 1969).Google Scholar
6.Krasnoselskii, M. A., Topological methods in the theory of nonlinear integral equations (Pergamon Press, New York, 1964).Google Scholar
7.Prodi, G. and Ambrosetti, A., Analisi non lineare (Scuola Normale Superiore, Pisa, 1973).Google Scholar
8.Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems, Eigenvalues of nonlinear problems pp. 141–195. (Cremonese, Rome, 1974).Google Scholar
9.Vainberg, M. M., Variational methods for the study of nonlinear operators (Holden-Day, San Francisco, 1964).Google Scholar
10.Mawhin, J. and Willem, M., Critical point theory and Hamiltonian systems (Springer, Berlin, 1989).CrossRefGoogle Scholar