Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations (Journal of Partial Differential Equations, 2018)
In this work, a characterization of the doubly-weighted Bohr spectrum of an almost periodic function is given. We showed precisely that such a spectrum is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the existence of doubly-weighted pseudo-almost periodic solutions to some classes of non-autonomous partial evolution equations.
Keywords: Evolution family; exponential dichotomy; acquistapace and Terreni conditions; doubly-weighted pseudo-almost periodic; evolution equation; nonautonomous equation