Investigation of a nonlocal Stieltjes type coupled boundary value problem of higher order nonlinear ordinary differential equations

We explore the existence criteria for solutions of a coupled system of two higher-order nonlinear ordinary differential equations supplemented with nonlocal and Stieltjes-type coupled boundary conditions. Such problems are useful in view of their occurrence in certain physical phenomena (see  Section ۱). In our first result, we apply the Leray-Schauder alternative to establish the existence of solutions to the given problem, while the second result deals with the uniqueness of solutions for the problem at hand, and it is based on Banach's fixed-point theorem.  Examples are included to illustrate the results obtained. Finally, we indicate some new results arising as special cases of the ones presented in this paper.

کلیدواژه ها:

Ordinary differential equations ، Coupled system ، nonlocal Stieltjes coupled boundary boundary conditions ، Fixed point