Vol. 70, No. 1, 1977

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Exponential representation of solutions to an abstract semi-linear differential equation

Glenn Francis Webb

Vol. 70 (1977), No. 1, 269–279
Abstract

It is shown that the solutions to the abstract differential equation u= (A + B)u, u(0) = x X, where X is a Banach space, A is a linear analytic semigroup generator, and B is Lipschitz continuous from the domain of a fractional power of A to X, have the exponential representation u(t) = limn→∞(I + t∕n(A + B))nx.

Mathematical Subject Classification
Primary: 34G05, 34G05
Secondary: 47D05
Milestones
Received: 28 January 1976
Published: 1 May 1977
Authors
Glenn Francis Webb
Department of Mathematics
Vanderbilt University
1326 Stevenson Center
Nashville TN 37240
United States