Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 425-436
Almost periodic mild solutions of a class of partial functional
1Department of Mathematics, University of Augsburg, Augsburg D-86135, Germany
2Department of Mathematics, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo 182, Japan
Received 10 May 1998
Copyright © 1998 Bernd Aulbach and Nguyen Van Minh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the existence of almost periodic mild solutions of a
class of partial functional differential equations via semilinear
almost periodic abstract functional differential equations of the form
To this end, we first associate with every almost periodic semilinear
equation a nonlinear semigroup in the space of almost periodic functions.
We then give sufficient conditions (in terms of the accretiveness of
the generator of this semigroup) for the existence of almost periodic
mild solutions of (**) as fixed points of the semigroup.
Those results are then carried over to equation (*).
The main results are stated under accretiveness conditions of the
function in terms of and Lipschitz conditions with respect to .