Webb, J.R.L. (2017) New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, 49(3), pp. 534-547. (doi: 10.1112/blms.12055)
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Abstract
Motivated by boundary value problems we give new results for a class of nonlinear Hammerstein integral operators acting in a cone to have a fixed point index equal to one. The idea is to allow the nonlinearity to be large on one part of its domains provided it is sufficiently small on a second part. Stronger results are obtained when the nonlinearity is decreasing on the second part of its domain. This allows new classes of nonlinearities to be treated and existence of a positive solution is established under weaker conditions than in previous works. The results are flexible and are not tied to any particular boundary conditions but can be applied to very many problems. We give several examples including applications to problems arising in chemical reactor theory.
Item Type: | Articles |
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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 |
Journal Name: | Bulletin of the London Mathematical Society |
Publisher: | Wiley |
ISSN: | 0024-6093 |
ISSN (Online): | 1469-2120 |
Published Online: | 21 April 2017 |
Copyright Holders: | Copyright © 2017 London Mathematical Society |
First Published: | First published in Bulletin of the London Mathematical Society 49(3): 534-547 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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