Abstract
There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a state-dependent functional integro-differential inclusion with delay nonlocal condition is studied. We, moreover, conclude the existence of solutions to the problem with the integral condition and the infinite-point boundary one. Some properties of the solutions are given. Finally, two examples illustrating the main result are presented.