On the Existence of Minimal and Maximal Solutions of Discontinuous Functional Sturm-liouville Boundary Value Problems

In Section 2, we give first an existence result for problems where the second, the functional argument u of g, is replaced in (1.1) by fixed functions v ∈ C(J), and study the dependence of solution sets of these problems on v. The so obtained results and a fixed point result for multifunctions proved recently in [7] are then used in Section 3 to derive existence results for minimal and maximal solutions of (1.1). Also in nonfunctional case we get new existence results. Because of weaker hypotheses than those assumed, for example, in [1, 3, 4, 5, 8, 9, 10], the fixed point results for single-valued operators do not apply.