some eigenvalue results for maximal monotone operators

we study the eigenvalue problem of the form 0 ∈ tx − λcx,

where x is a real reflexive banach space with its dual x^∗ and t : x ⊃ 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_μ. moreover, the solvability of the perturbed problem 0 ∈ tx + cx is discussed in an analogous method to the above problem.