Abstract
In this paper we develop criteria ensuring the existence and uniqueness of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal integral multi-point coupled boundary conditions on an arbitrary domain. The existence results are proved via Leray-Schauder alternative and Schauder fixed point theorem, while the existence of a unique solution is obtained by applying the Banach contraction mapping principle. Finally some examples are constructed for illustration of the obtained results.