Eigenvalue for Densely Defined (S+)‎L Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

Abstract EN

Let X be a real reflexive Banach space and let X∗ be its dual.

Let Ω⊂X be open and bounded such that 0∈Ω.

Let T:X⊃D(T)→2X∗ be maximal monotone with 0∈D(T) and 0∈T(0).

Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem Tx+λPx∋0, where the operator P:X⊃D(P)→X∗ is a single-valued of class (S+)L.

The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator P:X→2X∗ is multivalued and is investigated.