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A new criterion for the existence of multiple solutions in cones

Published online by Cambridge University Press:  20 September 2012

Daniel Franco ,
Gennaro Infante  and
Juan Perán
Daniel Franco
Affiliation:
Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, Madrid 28040, Spain ([email protected])
Gennaro Infante
Affiliation:
Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy ([email protected])
Juan Perán
Affiliation:
Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, Madrid 28040, Spain ([email protected])
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Abstract

We provide new sufficient conditions for the existence of multiple fixed points for a map between ordered Banach spaces. An interesting feature of this approach is that we require conditions not on two boundaries, but rather on one boundary and a point with some extra information on the monotonicity of the nonlinearity on a certain set. We apply our results to prove the existence of at least two positive solutions for a nonlinear boundary-value problem that models a thermostat.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 5 , October 2012 , pp. 1043 - 1050
Copyright
Copyright © Royal Society of Edinburgh 2012

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