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.
"Bounded solutions of nonlinear Cauchy problems." Abstr. Appl. Anal. 7 (12) 637 - 661, 24 December 2002. https://doi.org/10.1155/S1085337502208015