Egberts, Paul On the sum of maximal monotone operators and an application to a nonlinear integro-differential equation. (English) Zbl 0862.47028 Differ. Integral Equ. 6, No. 5, 1187-1194 (1993). This paper deals with the sum of a linear \(L\) and a nonlinear \(A\) maximal monotone operators in a Hilbert space. It is proved that under certain conditions the sum \(L+A\) with domain \(D(L+A)= D(L)\cap D(A)\) is maximal monotone as well. As an application existence and uniqueness result is proved for strong solutions of nonlinear integrodifferential equations. Reviewer: S.Tersian (Russe) Cited in 1 Document MSC: 47H05 Monotone operators and generalizations 47J25 Iterative procedures involving nonlinear operators 45K05 Integro-partial differential equations Keywords:sum; maximal monotone operators; strong solutions of nonlinear integrodifferential equations PDFBibTeX XMLCite \textit{P. Egberts}, Differ. Integral Equ. 6, No. 5, 1187--1194 (1993; Zbl 0862.47028)