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Optimal constants in a nonlocal boundary value problem. (English) Zbl 1153.34320
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.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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