Degree for weakly upper semicontinuous perturbations of quasi-<i>m</i>-accretive operators

In the paper we provide construction of a coincidence degree being homotopy invariant detecting existence solutions equations or inclusions form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an $m$-accretive operator in Banach space $ E$, $F\colon K\multimap weakly upper semicontinuous set-valued map constrained to open subset $U$ closed set $K\subset E$. Two different approaches will be presented. The theory applied show nontrivial positive some nonlinear second order partial differential with discontinuities.