We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: , , where is the infinitesimal generator of an exponentially stable -semigroup. An application is also given to illustrate the abstract existence theorem.
"Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations." Abstr. Appl. Anal. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/179525