Positive solutions for discontinuous problems with applications to $$\phi $$ ϕ -Laplacian equations

Abstract

We establish existence and localization of positive solutions for general discontinuous problems for which a Harnack-type inequality holds. In this way, a wide range of ordinary differential problems such as higher order boundary value problems or $$\phi $$ -Laplacian equations can be treated. In particular, we study the Dirichlet–Neumann problem involving the $$\phi $$ -Laplacian. Our results rely on Bohnenblust–Karlin fixed point theorem which is applied to a multivalued operator defined in a product space.