for the boundary value problem $\displaystyle (py')'+Vy=r$ where p,y,v and r functions of x. $\displaystyle y(a)=0=ky(b)+my'(b)$. the green functions G(x,t) on the domain {(x,t): $\displaystyle a\le x<t\le b$} is given by $\displaystyle G(x,t)=-u(x)v(t)/{p(x)W(u,v)(t)}$ where $\displaystyle u(a)=0=kv(b)+myv'(b)$. Write down the Green's function for the domain

{(x,t): $\displaystyle a\le t<x\le b$}

Why do we have minus sign here $\displaystyle G(x,t)=-u(x)v(t)/{p(x)W(u,v)(t)}$ how would the domain of this Green's function change if there was no minus sign?

thanks for any help.