Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators. (Q1867257)

In a reflexive Banach space, the authors obtain a general ``ranges of sums'' result involving a maximal monotone operator \(A\) and a densely defined finitely continuous quasibounded generalized pseudomonotone operator \(B\). This result improves [\textit{F. E. Browder}, J. Funct. Anal. 25, 356--365 (1977; Zbl 0358.47037)], concerning everywhere defined continuous and bounded operators \(B\). Extensions of this theory are given using the degree theory of \textit{A. G. Kartsatos} and \textit{I. V. Skrypnik} [Trans. Am. Math. Soc. 354, 1601--1630 (2002; Zbl 1005.47058)] concerning densely defined perturbations of nonlinear maximal monotone operators with \((S_{+})\)-condition. Applications to nonlinear parabolic problems on cylindrical domains are given.