The authors establish the following criterion for the existence of a positive solution to the boundary value problem (1) , , , .
Theorem. Suppose that ; ; ; and assume that there exist two distinct positive constants , such that
where is the Green’s function of the differential equation , with respect to the same boundary conditions as (1). Then (1) has at least one positive solution such that between and .
The authors apply this main result to establish several existence theorems of multiple positive solutions for some nonlinear (elliptic) differential equations.