Existence results for operator equations in abstract spaces and an application

In this paper we apply the recursion method presented in (Heikkilä and Lakshmikantham, 1994) to derive fixed point theorems and existence results for operator equations in partially ordered sets. The obtained results, combined with related results of (Heikkilä, 2002) are then applied to operator equations in ordered Hilbert spaces and to a functional elliptic boundary value problem.  2004 Elsevier Inc. All rights reserved