Supplementary material from "Degree for weakly upper semicontinuous perturbations of quasi-m-accretive operators. 3 September 2020"

In the paper, we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form Ax∈F(x),  x∈U, where A: D(A)\multimap E is an m-accretive operator in a Banach space E, F: K\multimap E is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K⊂E. Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities.This article is part of the theme issue ‘Topological degree and fixed-point theories in differential and difference equations’.