WEAKLY NONLOCAL BOUNDARY VALUE PROBLEMS WITH APPLICATION TO GEOLOGY

In many cases, groundwater flow in an unconfined aquifer can be simplified to a onedimensional Sturm-Liouville model of the form: x '' (t) + lambda x(t) = h(t) + epsilon f (x(t)), t is an element of (0, pi) subject to non-local boundary conditions x(0) = h(1) + epsilon eta(1)( x) and x(pi) = h(2) + epsilon eta(2)(x). In this paper, we study the existence of solutions to the above Sturm-Liouville problem under the assumption that epsilon is a small parameter. Our method will be analytical, utilizing the implicit function theorem and its generalizations.