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

Let X be a real reflexive Banach space with dual X∗. Let L : X ⊃ D(L)→ X∗ be densely defined, linear and maximal monotone. Let T : X ⊃ D(T ) → 2X∗, with 0 ∈ D(T ) and 0 ∈ T (0), be strongly quasibounded and maximal monotone, and C : X ⊃ D(C) → X∗ bounded, demicontinuous and of type (S+) w.r.t. D(L). A new topological degree theory has been developed for the sum L + T + C. This degree theory is an extension of the Berkovits–Mustonen theory (for T = 0) and an improvement of the work of Addou and Mermri (for T : X → 2X∗ bounded). Unbounded maximal monotone operators with 0 ∈ ˚D (T ) are strongly quasibounded and may be used with the new degree theory