Existence of a positive solution with concave and convex components for a system of boundary value problems

We prove the existence of at least one positive solution for a system of two nonlinear second-order differential equations with nonlocal boundary conditions. One component of the solution is a concave function, and the other one is a convex function. A recent hybrid Krasnosel’skiĭ– Schauder fixed point theorem is used to prove the existence of a positive solution. To illustrate the applicability of the obtained result, an example is considered.