Some eigenvalue results for maximal monotone operators

Abstract

We study the eigenvalue problem of the form 0 ∈ T x − λ C x , 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 ∈ T x + C x is discussed in an analogous method to the above problem.