Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: XaS integral D(T) -> 2 (X) * is a maximal monotone multi-valued operator and C: XaS integral D(C) -> X* is a generalized pseudomonotone quasibounded operator with L aS, D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 a T (x) + lambda C (x) , with a regularization method by means of the duality operator. Moreover, possible branches of eigensolutions to the above inclusion are discussed. Furthermore, we give a surjectivity result about the operator lambda T + C when lambda is not an eigenvalue for the pair (T, C), T being single-valued and densely defined.