Existence results for a self-adjoint coupled system of nonlinear second-order ordinary differential inclusions with nonlocal integral boundary conditions

A coupled system of nonlinear self-adjoint second-order ordinary differential inclusions supplemented with nonlocal non-separated coupled integral boundary conditions on an arbitrary domain is studied. The existence results for convex and non-convex valued maps involved in the given problem are proved by applying nonlinear alternative of Leray-Schauder for multi-valued maps, and Covitz-Nadler's fixed point theorem for contractive multi-valued maps, respectively. Illustrative examples for the obtained results are presented. The paper concludes with some interesting observations.