Existence results for singular strongly non-linear integro-differential BVPs on the half line

This work is devoted to the study of singular strongly non-linear integro-differential equations of the type (Formula presented.) where f is a Carathéodory function, Φ is a strictly increasing homeomorphism, and k is a non-negative integrable function, which is allowed to vanish on a set of zero Lebesgue measure, such that 1/k∈Llocp(R0+) for a certain p>1. By considering a suitable set of assumptions, including a Nagumo–Wintner growth condition, we prove existence and non-existence results for boundary value problems associated with the non-linear integro-differential equation of our interest in the sub-critical regime on the real half line.