A new topological degree theory for densely defined quasibounded (S˜+)-perturbations of multivalued maximal monotone operators in reflexive Banach spaces. (28th April 2005) - Kartsatos, Athanassios G.; Skrypnik, Igor V.
Abstract : LetX be an infinite-dimensional real reflexive Banach space with dual spaceX ∗ andG ⊂ X open and bounded. Assume thatX andX ∗ are locally uniformly convex. LetT : X ⊃ D ( T ) → 2 X ∗ be maximal monotone andC : X ⊃ D ( C ) → X ∗ quasibounded and of type( S ˜ + ) . Assume thatL ⊂ D ( C ), whereL is a dense subspace ofX, and0 ∈ T ( 0 ) . A new topological degree theory is introduced for the sumT + 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 perturbationsC . 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.