Positive solutions of a boundary value problem with integral boundary conditions

We consider boundary-value problems studied in a recent paper. We show that some existing theory developed by Webb and Infante applies to this problem and we use the known theory to show how to find improved estimates on parameters $mu^*, lambda^*$ so that some nonlinear differential equations, with nonlocal boundary conditions of integral type, have two positive solutions for all $lambda$ with $mu^*< lambda < lambda^*$.