TITLE

Solutions of nonlinear equations in cones and positive linear operators

AUTHOR(S)
Webb, J. R. L.
PUB. DATE
October 2010
SOURCE
Journal of the London Mathematical Society;Oct2010, Vol. 82 Issue 2, p420
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We introduce a modification of the concept of a cone invariant linear operator being u0-positive, a concept due to Krasnosel'skiÄ­. We show how this definition allows us to prove results closely related to some results for positive operators in a classic text of Krasnosel'skiÄ­. We also show how it can be used, in conjunction with the theory of a fixed-point index, to give some short proofs of existence and nonexistence of positive solutions for nonlinear maps. We prove a new fixed-point index result and show that it can be applied in cases where the previous theory is not applicable.
ACCESSION #
53882165

 

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