## Domain of Green's function

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} 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}

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.