Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T12:53:09.458Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)