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 Omega subset of E an open bounded subset, and let T-i : D(T-i) - 2(E*), i = 1, 2, be two maximal monotone mappings such that (Omega) over bar boolean AND D(T-1) boolean AND D(T-2) not equal empty set and 0 is not an element of U-t is an element of[0,U-1] [tT(1) + (1 - t)T-2](partial derivative Omega boolean AND (D(T-1) boolean OR D(T-2))). Under some additional assumptions we prove that deg (T-1, D(T-1) boolean AND Omega, 0) = deg (T-2, D(T-2) boolean AND Omega, 0). (C) 2008 Elsevier Inc. All rights reserved.