Multiple Positive Solutions of Some Boundary Value Problems

We study the existence of multiple positive solutions of the equations −u′′=ƒ(t, u), subject to linear boundary conditions. We show that there are at least two positive solutions if ƒ(t, u) is superlinear at one end point (zero or infinity) and sublinear at the other. Applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus.