Degree theory for monotone type mappings in non-reflexive Banach spaces

Let E be a real separable Banach space, E∗ the dual space of E, and Ω⊂E an open bounded subset, and let T:D(T)⊆E→2E∗ be a mapping of class (S+)L with D(T)∩Ω⁄=0̸ see Definition 1.2. A degree theory is constructed for such a mapping.