Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace–Terreni conditions and exponential dichotomy, the existence of (μ,ν)- pseudo almost periodic (respectively, (μ,ν)-pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper.
@article{1274,
title = {Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory},
journal = {CUBO, A Mathematical Journal},
volume = {16},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/1274}
}
Diagana, Toka; Ezzinbi, Khalil; Miraoui, Mohsen. Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory. CUBO, A Mathematical Journal, Tome 16 (2014) 31 p. http://gdmltest.u-ga.fr/item/1274/