Positive solutions of nonlinear differential equations with Riemann-Stieltjes boundary conditions

We study the existence of positive solutions for some nonlinear second order boundary value problems with nonlocal boundary conditions. The key boundary condition considered is of the form u ( 1) = alpha [u'], where a is a linear functional on C [0, 1], that is, is given by a Riemann- Stieltjes integral alpha[nu] = integral(1)(0) nu (s) dA (s) where A is a function of bounded variation. It is important in our case that dA is not a positive measure but can be sign changing.