Invariance of domain and eigenvalues for perturbations of densely defined linear maximal monotone operators

Let X be a real reflexive Banach space with dual X*. Let L : X superset of D(L) --> X* be densely defined linear maximal monotone. Let T : X superset of D(L) -->2(X)* be maximal monotone with 0 is an element of (D) over circle (T) and 0 is an element of T(0), and C : X superset of D(C) --> X* bounded, demicontinuous and of type (S+) w.r.t. D(L). An invariance of domain result is established for the sum L + T + C. An eigenvalue problem of the type Lx + Tx + C(lambda, x) (sic) 0 is also solved, where T is now maximal monotone and strongly quasibounded with 0 is an element of T(0) and C (lambda, .), lambda > 0 is like C above. The recent topological degree theory of the authors is used, utilizing the graph norm topology on D(L), along with the methodology of Berkovits and Mustonen and recent invariance of domain and eigenvalue results by Kartsatos and Skrypnik. The results are original even in the case T = 0. Possible applications to time-dependent problems are also included.