Multiplicity of positive solutions of even-order nonhomogeneous boundary value problems.

Abstract

In this work, we discuss multiplicity results for nonhomogeneous even-order boundary value problems on both discrete and continuous domains. We develop a method for establishing existence of positive solutions by transforming even-order problems into a series of second order problems satisfying homogeneous boundary conditions. We then construct a sequence of lemmas which give contraction and expansion relationships within a cone. This allows us to apply the Guo-Krasnosel'skii Fixed Point Theorem which, in turn, guarantees several positive solutions.