Topological analysis of doubly nonlocal boundary value problems

We consider both Hammerstein integral equations and nonlocal boundary value problems in possession of two different nonlocal elements. The first occurs in the differential equation itself and takes the form parallel to u parallel to(q)(q). The second occurs in the boundary condition and takes the form of a Stieltjes integral. Because the nonlocal elements are not necessarily related, a careful analysis is required to control each nonlocal element simultaneously. Topological fixed point theory is used to deduce existence of at least one positive solution to the boundary value problem. And we illustrate the application of the results with an example.