TITLE

Representations of compact linear operators in Banach spaces and nonlinear eigenvalue problems

AUTHOR(S)
Edmunds, D. E.; Evans, W. D.; Harris, D. J.
PUB. DATE
August 2008
SOURCE
Journal of the London Mathematical Society;Aug2008, Vol. 78 Issue 1, p65
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let X and Y be reflexive Banach spaces with strictly convex duals, and let T be a compact linear map from X to Y. It is shown that a certain nonlinear equation, involving T and its adjoint, has a normalised solution (an ‘eigenvector’) corresponding to an ‘eigenvalue’, and that the same is true for each member of a countable family of similar equations involving the restrictions of T to certain subspaces of X. The action of T can be described in terms of these ‘eigenvectors’. There are applications to the p-Laplacian, the p-biharmonic operator and integral operators of Hardy type.
ACCESSION #
44398874

 

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