On the homotopy property of topological degree for maximal monotone mappings (Q1004421)

The purpose of the present paper is to study a homotopy property of the degree for maximal monotone mappings, and fill the lack of this important property in one of the papers of the first author [Appl.\ Math.\ Mech., Engl.\ Ed.\ 11, No.\,5, 441--454 (1990; Zbl 0895.47044)]. The homotopy property is presented in Theorem 2.9, while a sufficient condition for the homotopy to have no zeros on a boundary of the set is given in Theorem 2.1. One assumes that \(0\in Tx_0\cap Sx_0\), for some \(x_0\), and \(\inf_{x\in\partial\Omega}\|x\|>\|x_0\|\)