Apply the Sturm-Liouville Problem With Green’s Function to Linear System

In this paper, we will study the Sturm-Liouville problem, we find the eigenvalues are the solution of the Sturm-Liouville problem and the eigenfunctions are corresponding solutions. Thus, we study construction of the Green’s function to solving the first order differential n-dimensional linear system, and application for Fourier series, and we show that the Green’s function solution to the twoand three-dimensional Laplace and Poisson equations.