Multiplicity Results for Operator Systems via Fixed Point Index

Abstract

We establish existence, localization and multiplicity results of positive solutions for general operator systems in ordered Banach spaces. Our main tool is the fixed point index in cones which we compute in suitable relatively open sets. In this context, each component of the fixed point operator can satisfy either the expansion condition or the compression condition. If some component of the operator is expansive, then we obtain multiplicity results. As an application, new results concerning systems of Hammerstein equations and systems of -Laplace equations are deduced.