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 related linear operator. We also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions. (c) 2005 Elsevier Ltd. All rights reserved.