Degree for weakly upper semicontinuous perturbations of quasi-m-accretive operators

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 is an element of F(x), x is an element of U, where A:D(A) (sic) E is an m-accretive operator in a Banach space E, F:K(sic)E is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K subset of 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'.

Automated summary

In this paper, a coincidence degree construction is provided as a homotopy invariant for detecting the existence of solutions of equations. 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.