doi:10.3390/math9050474engAbadias, L.Alvarez, EdgardoGrau, Rogelio(w, c)-periodic mild solutions to non-autonomous abstract differential equationsART-2021-124313We investigate the semi-linear, non-autonomous, first-order abstract differential equation x′(t)=A(t)x(t)+f(t,x(t),φ[α(t,x(t))]),t∈R. We obtain results on existence and uniqueness of (ω,c)-periodic (second-kind periodic) mild solutions, assuming that A(t) satisfies the so-called Acquistapace–Terreni conditions and the homogeneous associated problem has an integrable dichotomy. A new composition theorem and further regularity theorems are given.2021http://zaguan.unizar.es/record/10210710.3390/math9050474http://zaguan.unizar.es/record/102107oai:zaguan.unizar.es:102107info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00info:eu-repo/grantAgreement/ES/UZ/JIUZ-2019-CIE-01Mathematics 9, 5 (2021), 474 [15 pp.]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess