A new topological degree theory for densely defined quasibounded ( S ˜ + ) -perturbations of multivalued maximal monotone operators in reflexive Banach spaces

Let X be an infinite-dimensional real reflexive Banach space with dual space X ∗ and G ⊂ X open and bounded. Assume that X and X ∗ are locally uniformly convex. Let T : X ⊃ D ( T ) → 2 X ∗ be maximal monotone and C : X ⊃ D ( C ) → X ∗ quasibounded and of type ( S ˜ + ) . Assume that L ⊂ D ( C ) , where L is a dense subspace of X , and 0 ∈ T ( 0 ) . A new topological degree theory is introduced for the sum T + C . Browder's degree theory has thus been extended to densely defined perturbations of maximal monotone operators while results of Browder and Hess have been extended to various classes of single-valued densely defined generalized pseudomonotone perturbations C . Although the main results are of theoretical nature, possible applications of the new degree theory are given for several other theoretical problems in nonlinear functional analysis.