Optimal constants in a nonlocal boundary value problem

We give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions, that arise as a model of a thermostat. We obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a relat...

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Bibliographic Details
Published in:Nonlinear analysis 2005-11, Vol.63 (5), p.672-685
Main Author: Webb, J.R.L.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Optimal constants
Ordinary differential equations
Positive solutions
Principal eigenvalue
Sciences and techniques of general use
Thermostat model
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Summary:We give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions, that arise as a model of a thermostat. We obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a related linear operator. We also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2005.02.055