On the Green function of higher order differential equation with normal operator coefficients on the semi-axis

Abstract

In the paper we study the Green function for $2n$-th order differential equation with a normal operator coefficient on the semi-axis. To this end, at first we construct the Green function of the equation with "frozen" coefficients. Then we use the Levi method and obtain an integral equation for the Green function of the given equation. We prove the solvability of the integral equation. Using the integral equation we establish the main properties of the Green function.