Some eigenvalue results for maximal monotone operators

We study the eigenvalue problem of the form 0 is an element of Tx - lambda Cx, where X is a real reflexive Banach space with its dual X* and T : X superset of D(T) -> 2(X)* is a maximal monotone multi-valued operator and C : D(T) -> X* is a not necessarily continuous single-valued operator. Using the index theory for countably condensing operators, we extend some related results of Kartsatos to the countably condensing case instead of compactness of the approximant J(mu). Moreover, the solvability of the perturbed problem 0 is an element of Tx + Cx is discussed in an analogous method to the above problem. (C) 2011 Elsevier Ltd. All rights reserved.