Existence of Doubly-Weighted Pseudo Almost Periodic Solutions to Some Classes of Nonautonomous Differential Equations

The main objective of this paper is twofold. We first show that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the problem which consists of the existence of doubly-weighted pseudo-almost periodic solutions to some nonautonomous abstract differential equations.