Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators

Let X be a real reflexive Banach space and A:X-->2(X*) be maximal monotone. Let B : X-->2(X*) be quasibounded, finitely continuous and generalized pseudomonotone with X' subset of D(B), where X' is a dense subspace of X such that X' boolean AND D(A) not equal 0. Let S subset of X*. Conditions are given under which S subset of <(R(A + B))over bar> and int S subset of int R(A + B). Results of Browder concerning everywhere defined continuous and bounded operators B are improved. Extensions of this theory are also given using the degree theory of the last two authors concerning densely defined perturbations of nonlinear maximal monotone operators which satisfy a generalized (S+)-condition. Applications of this extended theory are given involving nonlinear parabolic problems on cylindrical domains. (C) 2002 Elsevier Science (USA). All rights reserved.