Existence of S-asymptotically ω-periodic solutions to abstract integro-differential equations

Asymptotic periodicity for hyperbolic evolution equations and applications

“…A similar result as Theorem 4.40 was obtained in [39] for obtaining the existence and uniqueness of Sasymptotically ω-periodic mild solutions for a class of abstract integro-differential equations. It is easy to see that by using the same proof of Theorem 4.38 we can get existence and uniqueness of PSAP ω -solutions for these type of integro-differential equations.…”

“…The proof is based on an adaptation of the ideas developed in recent work of dos Santos and Henríquez [39,Theorem 3.2]. Now we divide the proof into several steps.…”

“…We refer the reader to [14,[17][18][19]24,39]. In addition, in [37] a new space of S-asymptotically ω-periodic functions was introduced.…”