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On the sum of maximal monotone operators and an application to a nonlinear integro-differential equation. (English) Zbl 0862.47028

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)

MSC:

47H05 Monotone operators and generalizations
47J25 Iterative procedures involving nonlinear operators
45K05 Integro-partial differential equations
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