Abstract and Applied Analysis
Volume 7 (2002), Issue 12, Pages 637-661
Bounded solutions of nonlinear Cauchy problems
FB Mathematik, Universität Essen, Essen D-45117, Germany
Received 28 February 2001
Copyright © 2002 Josef Kreulich. 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.
For a given closed and translation invariant subspace
of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions
to the equation , or of solutions asymptotically close to for the inhomogeneous differential equation , in general Banach spaces, where
denotes a possibly nonlinear accretive generator of a semigroup. Particular examples for the space
are spaces of functions with various almost periodicity
properties and more general types of asymptotic behavior.