Ahmed Alsaedi, Amal Almalki, Sotiris K. Ntouyas, Bashir Ahmad, and Ravi P. Agarwal
Existence Results for a Self-adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal  Non-Separated Integral  Boundary Conditions
Dynamic Systems and Applications 30 (2021) No. 9, 1479-1501

https://doi.org/10.46719/dsa202130.09.06

ABSTRACT.
In this article, we develop the existence theory for a self-adjoint coupled system of nonlinear ordinary
differential equations supplemented with nonlocal non-separated integral boundary conditions on an arbitrary domain. The two existence results depend on the Leray-Schauder alternative and Schauder fixed point theorem, while the uniqueness result relies on the Banach contraction mapping principle. For the illustration of the obtained result, we constructed several examples in the last section.

AMS (MOS) Subject Classification. 34B10, 34B15, 47H10.