id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-67	El Attaouy, Meryem; Ezzinbi, Khalil; ˜N'Guerekata, Gaston Mandata	Reduction principle for partial functional differential equation without compactness	2023	17	.pdf	application/pdf	6665	355	73	In this work we are interested in investigating the existence of almost automor- phic and almost periodic solutions for the partial functional differential equation x′(t) = Ax(t) + L(xt) + f(t) for t ∈ R, (1.3) whereA is the infinitesimal generator of a strongly continuous semigroup of bounded linear operators T (t) on a Banach space X. x(t) ∈ X, L is a bounded linear opera- tor from C([−r, 0], X) to X with C([−r, 0], X) is the space of continuous functions from [−r, 0] to X endowed with the uniform norm topology and r > 0. dξ ] (0), for t ∈ R, is a mild solution of (1.3) on R. As a consequence of the above, we establish the following fundamental reduction principle which allows us to prove the existence of an almost automorphic and almost periodic solution of the (1.3).	cache/ejde-67.pdf	txt/ejde-67.txt