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

Why do we have minus sign here 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.