The authors established existence of multiple solutions of nonlinear differential equations of the form
where and are nonnegative functions, subject to
or other nonlocal boundary conditions. They study the problems via new results for a perturbed integral equations of the form
where are linear functionals given by Stieltjes integrals but not assumed to be positive for all positive . -point boundary value problems are special cases and they obtain sharp conditions on the coefficients, which allows some of them to have opposite signs.