On green s function of an w-point boundary value problem

The Green’s function g (xf s) for an n-point boundary value problem, yv '(%)= 0, y(a2) = y(a2) = y(a2) = 0 is explicitly given. As a tool for discussing sgng(fx, s) on the square [a2ajx [a2a2], some results about polynomials with coefficients as symmetric functions of a*s are obtained. It is shown thatfa nlrfsis a suitable polynomial in x. Applications to n-point boundary value problems and lower bounds for a (m n) are included. © 1973 American Mathematical Society.