Second order three boundary value problem in Banach spaces via Henstock and Henstock–Kurzweil–Pettis integral

Existence theorems and some properties of solutions set of three boundary value second order differential equations and inclusions in Banach spaces are obtained under Henstock, respectively Henstock–Kurzweil–Pettis integrability assumptions. Our results extend those obtained by Azzam, Castaing and Thibault in the Bochner integrability setting and in the Pettis integrability one. The continuity of the (unique) solution with respect to a parameter in the single-valued case is also studied.