Some eigenvalue results for maximal monotone operators

We study the eigenvalue problem of the form 0∈Tx−λCx,0∈Tx−λCx, where XX is a real reflexive Banach space with its dual X∗X∗ and T:X⊃D(T)→2X∗T:X⊃D(T)→2X∗ is a maximal monotone multi-valued operator and C:D(T)→X∗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 JμJμ. Moreover, the solvability of the perturbed problem 0∈Tx+Cx0∈Tx+Cx is discussed in an analogous method to the above problem.