Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-28T16:23:19.230Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear eigenvalue problems

Published online by Cambridge University Press:  17 April 2009

L.Ju. Fradkin  and
G.C. Wake
L.Ju. Fradkin
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand.
G.C. Wake
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand.
Rights & Permissions [Opens in a new window]

Abstract

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.

The object of this paper is to prove two new results on the nature of the spectrum of a class of nonlinear elliptic eigenvalue problems. In the first case, sufficient conditions are given for which the spectrum is bounded and, in the second case, conditions are given for which the spectrum is open.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 467 - 472
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Amann, Herbert, “On the existence of positive solutions of nonlinear elliptic boundary value problems”, Indiana Univ. Math. J. 21 (1971), 125–146.CrossRefGoogle Scholar
[2]Amann, Herbert, “Positive solutions of convex nonlinear eigenvalue problems”, Indiana Univ. Math. J. (to appear).Google Scholar
[3]Keller, H.B., “Some positone problems suggested by nonlinear heat generation”, Bifurcation theory and nonlinear eigenvalue problems, 217–255 (Benjamin, New York, Amsterdam, 1969).Google Scholar
[4]Keller, Herbert B. and Cohen, Donald S., “Some positone problems suggested by nonlinear heat generation”, J. Math. Mech. 16 (1967), 1361–1376.Google Scholar
[5]Ladyzhenskaya, Olga A. and Ural'tseva, Nina N., Linear and quasilinear elliptic equations (Mathematics in Science and Engineering, 46. Translated by Technica, Scripta. Academic Press, New York and London, 1968).Google Scholar