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

Glenn Francis Webb

Vol. 70 (1977), No. 1, 269–279

DOI: 10.2140/pjm.1977.70.269

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) = lim_n→∞(I + t∕n(A + B))⁻ⁿx.

Mathematical Subject Classification

Primary: 34G05, 34G05

Secondary: 47D05

Milestones

Received: 28 January 1976

Published: 1 May 1977