On the homotopy property of topological degree for maximal monotone mappings

Let E be a real reflexive Banach space, E∗ the dual space of E, and Ω⊂E an open bounded subset, and let Ti:D(Ti)→2E∗, i=1,2, be two maximal monotone mappings such that Ω¯∩D(T1)∩D(T2)≠∅ and 0∉∪t∈[0,1][tT1+(1-t)T2](∂Ω∩(D(T1)∪D(T2))). Under some additional assumptions we prove that deg(T1,D(T1)∩Ω,0)=deg(T2,D(T2)∩Ω,0).