RANGE OF PERTURBED MAXIMAL MONOTONE AND M-ACCRETIVE OPERATORS IN BANACH SPACES

摘要

A more comprehensive and unified theory is developed for the solvability of the inclusions S subset of R(A + B), intS subset of R(A + B), where A : X superset of D(A) --> 2(Y), B : X superset of D(B) --> Y and S subset of X. Here, X is a real Banach space and Y = X or Y = X*. Mainly, A is either maximal monotone or m-accretive, and B is either pseudo-monotone or compact. Cases are also considered where A has compact resolvents and B is continuous and bounded. These results are then used to obtain more concrete sets in the ranges of sums of such operators A and B. Various results of Browder, Calvert and Gupta, Gupta, Gupta and Hess; and Kartsatos are improved and/or extended. The methods involve the application of a basic result of Browder, concerning pseudo-monotone perturation of maximal monotone operators, and the Leray-Schauder degree theory. [References: 24]