Ranges of Operators of Monotone Type in Banach Space

Let X be a reflexive Banach space with both X and X* locally uniformly convex. Let G ⊂ X be open, bounded, and convex, and T: Ḡ → X* an operator of monotone type. By degree theory of operators of type (S+), certain range properties of T are established. The results are applied to the study of existence of a zero of T under various boundary conditions