Calculation of the greens function of boundary value problems for linear ordinary differential equations

Abstract

The Greens function is widely used in solving boundary value problems for differential equations, to which many mathematical and physical problems are reduced. In particular, solutions of partial differential equations by the Fourier method are reduced to boundary value problems for ordinary differential equations. Lets note that using the Greens function for a homogeneous problem, it is possible to calculate the solution of an inhomogeneous differential equation. Also, using the Greens function, one can solve the problem of finding eigenvalues, which are very relevant in quantum field theory