Existence theory for coupled nonlinear third-order ordinary differential equations with nonlocal multi-point anti-periodic type boundary conditions on an arbitrary domain

Abstract

In this paper, we derive existence and uniqueness results for a coupled system of nonlinear third order ordinary differential equations equipped with nonlocal multi-point anti-periodic type coupled boundary conditions. Leray-Schauder alternative and Banach contraction mapping principle are the main tools of our study. Examples are constructed for illustrating the obtained results. Under appropriate conditions, our results correspond to the ones for an ant-periodic boundary value problem of nonlinear third order ordinary differential equations.