Invariance of domain and eigenvalues for perturbations of densely defined linear maximal monotone operators

Abstract

Let be a real reflexive Banach space with dual . Let be densely defined linear maximal monotone. Let be maximal monotone with and and bounded, demicontinuous and of type w.r.t. . An invariance of domain result is established for the sum . An eigenvalue problem of the type is also solved, where is now maximal monotone and strongly quasibounded with and is like above. The recent topological degree theory of the authors is used, utilizing the graph norm topology on along with the methodology of Berkovits and Mustonen and recent invariance of domain and eigenvalue results by Kartsatos and Skrypnik. The results are original even in the case Possible applications to time-dependent problems are also included.

Keywords:

• topological degree theory
• linear maximal monotone operator
• strongly quasibounded maximal monotone operator
• demicontinuous operator of type

AMS Subject Classifications:

• Primary 47H14
• Secondary 47H05
• 47H11