A non-local problem of the second king for an ordinary second-order differential equation with the Nakhushev differentiation operator

In this paper, we study an ordinary second-order differential equation with the Nakhushev operator in the lower terms. The Nakhushev differentiation operator belongs to the class of continuously distributed differentiation operators. For this equation, a non-local boundary value problem with the Ilyin-Moiseev condition of the second kind is considered. The Ilyin-Moiseev condition of the second kind connects the value of the first derivative of the desired function at the right end of the interval, where the equation is set, with the values of the first derivative of the desired function at the inner (several) points of the interval. The Green function method is used to find a solution to the problem under study, construct the corresponding Green function, and study its properties.