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New fixed point index results and nonlinear boundary value problems
Author(s) -
Webb J. R. L.
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12055
Subject(s) - fixed point index , mathematics , nonlinear system , boundary value problem , class (philosophy) , domain (mathematical analysis) , point (geometry) , mathematical analysis , index (typography) , fixed point theorem , cone (formal languages) , fixed point , value (mathematics) , boundary (topology) , geometry , algorithm , computer science , statistics , physics , quantum mechanics , artificial intelligence , world wide web
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.