EXERCISE
Find Green's function $G(x,y:x_0,y_0)$ of the problem:
$ΔG(x,y:x_0,y_0)=-δ(x-x_0)δ(y-y_0), x, x_0\in \mathbf{R} , y, y_0 \in (0,\infty)$
$G(x,0:x_0,y_0)=0, x\in \mathbf{R}$
To tell the truth I don't know even how to start this exercise as I don't have any experience in this kind of exercises.
So how can I solve this exercise?I know that I haven't done any attempt here but I really don't how to use green functions in these exercises!
I would really appreciate a thorough solution and explanation or any hint here since I've just started working on these problems.
Thanks, in advance!