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)→X∗2, 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→X∗2 bounded). Unbounded maximal monotone operators with are strongly quasibounded and may be used with the new degree theory.