Strongly quasibounded maximal monotone perturbations for the Berkovits–Mustonen topological degree theory

A New Topological Degree Theory for Densely Defined Quasibounded (s̃+)-perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

Let X be an infinite-dimensional real reflexive Banach space with dual space X∗ and G⊂ X open and bounded. Assume that X and X∗ are locally uniformly convex. Let T : X ⊃ D(T) → 2X be maximal monotone and C : X ⊃ D(C) → X∗ quasibounded and of type (S̃+). Assume that L ⊂ D(C), where L is a dense subspace of X , and 0 ∈ T(0). A new topological degree theory is introduced for the sum T +C. Browder’s...

Eigenvalues of quasibounded maximal monotone operators

0 ∈ Tx + λCx, where T : D(T )⊂ X → 2X is a strongly quasibounded maximal monotone operator and C : D(C)⊂ X → X∗ satisfies the condition (S+)D(C) with L⊂ D(C). The method of approach is to use a topological degree theory for (S+)L-perturbations of strongly quasibounded maximal monotone operators, recently developed by Kartsatos and Quarcoo. Moreover, applying degree theory, a variant of the Fred...

Topological Degree for Maximal Monotone Operators and Application to Parametric Optimization Problems 1

The generalized topological degree theory is based on the Brouwer and Leray-Schauder degrees. It can be deened for general classes of mappings. The purpose of this article is twofold. One goal is to deene the topological degree for maximal monotone operators. Particular attention is paid to the continuation methods for this kind of operators and real functions of convex type. This allows us to ...

Almost Global Convergence in Singular Perturbations of Strongly Monotone Systems

This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems.

Perturbations of Nonlinear Maximal Monotone Sets in Banach Space *