Solutions of nonlinear equations in cones and positive linear operators

Webb, J.R.L. (2010) Solutions of nonlinear equations in cones and positive linear operators. Journal of the London Mathematical Society, 82(2), pp. 420-436. (doi: 10.1112/jlms/jdq037)

Abstract

We introduce a modification of the concept of a cone invariant linear operator being u(0)-positive, a concept due to Krasnosel'ski. We show how this definition allows us to prove results closely related to some results for positive operators in a classic text of Krasnosel'ski. 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Webb, Professor Jeffrey
• Authors: Webb, J.R.L.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of the London Mathematical Society
• ISSN: 0024-6107