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Continuous nonlinear perturbations of linear accretive operators in banach spaces

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
10
Issue
2
Identifiers
DOI: 10.1016/0022-1236(72)90048-1

Abstract

Abstract Let A be a linear, closed, densely defined m-accretive operator from a Banach space X to itself, and let T( t), t ⩾ 0, be the semigroup of operators which has − A as its infinitesimal generator. Let B be a nonlinear, continuous, everywhere defined accretive operator from X to itself, and let S( t), t ⩾ 0, be the semigroup of nonlinear operators which has − B as its infinitesimal generator. It is shown that for all x ϵ X, t ⩾ 0, lim n → ∞(T( t n ) S( t n )) nx = U(t)x exists, U(t)x = T(t)x − ∝ 0 t T(t − s) BU(s) x ds, and U(t), t ⩾ 0 , is a strongly continuous semigroup of nonlinear contractions on X. It is shown also that −( A + B) is the infinitesimal generator of U( t), t ⩾ 0, and A + B is m-accretive on X.

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