New fixed point index results and nonlinear boundary value problems

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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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
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
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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