Componentwise localization of solutions to systems of operator inclusions via Harnack type inequalities

Abstract

We establish compression-expansion type fixed point theorems for systems of operator inclusions with decomposable multivalued maps. The approach is vectorial allowing to localize individually the components of solutions and to obtain multiple solutions with multiplicity not necessarily concerned with all components of the solution. A general scheme of applicability of the theory is elaborated based on Harnack type inequalities and illustrated on systems of differential inclusions with one-dimentional ϕ-Laplacian.